Topology Books
World Scientific Publishing Co Pte Ltd Topology In Condensed Matter: An Introduction
Book SynopsisThis text serves as a pedagogical introduction to the theoretical concepts on application of topology in condensed matter systems. It covers an introduction to basic concepts of topology, emphasizes the relation of geometric concepts such as the Berry phase to topology, having in mind applications in condensed matter. In addition to describing two basic systems such as topological insulators and topological superconductors, it also reviews topological spin systems and photonic systems. It also describes the use of quantum information concepts in the context of topological phases and phase transitions, and the effect of non-equilibrium perturbations on topological systems.This book provides a comprehensive introduction to topological insulators, topological superconductors and topological semimetals. It includes all the mathematical background required for the subject. There are very few books with such a coverage in the market.
£85.50
World Scientific Publishing Co Pte Ltd Elementary Topology And Applications
Book SynopsisThe textbook is a very good start into the mathematical field of topology. A variety of topological concepts with some elementary applications are introduced. It is organized in such a way that the reader gets to significant applications quickly.This revised version corrects the many discrepancies in the earlier edition. The emphasis is on the geometric understanding and the use of new concepts, indicating that topology is really the language of modern mathematics.
£52.25
World Scientific Publishing Co Pte Ltd Metric Space Topology: Examples, Exercises And
Book SynopsisThis introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers.In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially conducive to the understanding of the materials. This serves to give an insightful view of the intricate problems, as well as a clue or a direction to formulate rigorous arguments.The learning outcomes include:
£121.50
World Scientific Publishing Company Topological Structure Of Road Networks Models And
Book Synopsis
£90.00
Springer Verlag, Singapore Differential Geometry of Curves and Surfaces
Book SynopsisThis book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka. There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss–Bonnet Theorem; and 5. Minimal Surfaces. Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures — the Gaussian curvature K and the mean curvature H —are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes’ theorem for a domain. Then the Gauss–Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number χ(S). Here again, many illustrations are provided to facilitate the reader’s understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2. Trade Review“There is a wealth of excellent text books on the differential geometry of curves and surfaces. A rare jewel among them is the recent translation of a Japanese classic written by Shoshichi Kobayaschi … . This volume is a superb addition to the current literature on the geometry of curves and surfaces, and it is of major interest for classroom study, as well for general use as a reference and eventually for self-study.” (Bogdan D. Suceavă, The Mathematical Intelligencer, Vol. 44 (1), March 2022)“This is an excellent book written in a clear and precise style. The entire material is carefully developed, a lot of beautiful examples supporting the understanding. This is certainly a book that strongly motivates the reader to continue studying differential geometry, passing from the case of curves and surfaces in 3-dimensional Euclidean space to manifolds.” (Gabriel Eduard Vilcu, zbMATH 1437.53001, 2020)“The book reaches admirable destinations with few formal prerequisites and contains enough material for a leisurely one-semester undergraduate course.” (MAA Reviews, March 8, 2020)Table of ContentsPlane Curves and Space Curves.- Local Theory of Surfaces in the Space.- Geometry of Surfaces.- The Gauss-Bonnet Theorem.- Minimal Surfaces.
£31.49
Springer Verlag, Singapore Topological Dynamics and Topological Data
Book SynopsisThis book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.Table of ContentsH. Bruin, An Overview of Unimodal Inverse Limit Spaces.- B. Barany, M. Rams, K. Simon, Dimension Theory of Some Non Markovian Rapellers Part I: A General Introduction.- B. Barany, M. Rams, K. Simon, Dimension Theory of Some Non Markovian Repellers: Part II: Dynamically Defined Function Graphs.- K. Lesniak, Iterated Function Systems – A Topological Approach Attractors.- H. Kato, Zero Dimensional Covers of Dynamical Systems.- H. Kato, Chaotic Continua in Chaotic Dynamical Systems.- R. L. Devaney, S. M. Marotta, Mandelpinski Necklaces in the Parameter Planes of Rational Maps.- Kit C Chan, Some Examples of Hypercyclic Operators and Universal Sequences of Operators.- Kit C Chan, Some Basic Properties of Hypercyclic Operators.- Kit C Chan, The Testing Ground of Weighted Shift Operators for Hypercyclicity.- D. Drozdov, M. Samuel, A. Tetenov, On -deformations of Polygonal Dendrites.- A. Tetenov, K. Kamalutdinov, V. Aseev, General Position Theorems and its Applications.- A. Raj P, V. Kumar P B, The nth iterate of a map with dense orbit.- Aswathy R K, S. Mathew, Finite Products of Irregular Iterated Function Systems and Their Separation Properties.- A. Akbar, Mubeena T, Periodic Points of N-dimensional Toral Automorphisms.- S. Jose, V. Kumar P B, Julia Sets in Topological Spaces.- K U Sreeja, V. Kumar P B, Ramkumar P B, Julia, Sets of Some Graphs Using Independence Polynomials.- P. Frosini, An Introduction to the Notion of Natural Pseudo Distance in Topological Data Analysis.- A. Cerri, P. Frosini, A Brief Introduction to Multidimensional Persistent Betti Numbers.- N. Quercioli, Some New Methods to Build Group Equivariant Non Expansive Operators in TDA.- Y. Dabaghian, Topological Stability of the Hippocampal Spatial Map and Synaptic Transience.- A. Jacob, Ramkumar P B, Intuitionistic Fuzzy Graph Morphological Topology.- A. G. Pillai, Ramkumar P B, Some Properties of the Bitopological Space Associated with the 3-Uniform Semigraph of Cycle graph.- D. Chandran R, Ramkumar P B, Hypergraph Topology.
£143.99
Springer Verlag, Singapore Basic Topology 1: Metric Spaces and General
Book SynopsisThis first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.Trade Review“With an encyclopedic range of topics and terse exposition, Basic Topology 1 may make a reasonable reference for self-motivated learners … .” (Timothy Clark, MAA Reviews, March 20, 2023)Table of Contents1. Prerequisites: Sets, Algebraic Systems, and Classical Analysis.- 2. Metric Spaces and Normed Linear Spaces.- 3. Topological Spaces and Continuous Maps.- 4. Separation Axioms.- 5. Compactness and Connectedness.- 6. Real-valued Continuous Functions.- 7. Countability, Separability and Embedding.- 8. Brief History of General Topology.
£53.99
Springer Verlag, Singapore Basic Topology 3: Algebraic Topology and Topology
Book SynopsisThis third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.Table of Contents1. Prerequisite Concepts of Topology, Algebra and Category Theory.- 2. Homotopy Theory: Fundamental and Higher Homotopy Groups.- 3. Homology and Cohomology Theories: An Axiomatic Approach with Consequences.- 4. Topology of Fiber Bundles.- 5. Homotopy Theory of Bundles.- 6. Some Applications of Algebraic Topology.- 7. Brief History on Algebraic Topology and Fiber Bundles.
£49.49
Springer Verlag, Singapore Basic Topology 2: Topological Groups, Topology
Book SynopsisThis second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.Table of Contents1. Background on Topology, Analysis and Algebra.- 2. Topological Groups.- 3. Topology of Manifolds.- 4. Lie Groups and Lie Algebra.- 5. Brief History of Topological Groups, Manifold and Lie Groups.
£40.49
World Scientific Publishing Co Pte Ltd Geometric And Topological Methods For Quantum
Book SynopsisThis volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.Table of ContentsNoncommutative Geometry: Hopf Algebras in Noncommutative Geometry (J C Varilly); The Noncommutative Geometry of Aperiodic Solids (J Bellissard); Noncommutative Geometry and Abstract Integration Theory (M-T Benameur); Topological Field Theory: Introduction to Quantum Invariants of 3-Manifolds, Topological Quantum Field Theories and Modular Categories (C Blanchet); An Introduction to Donaldson-Witten Theory (M Marino); Supergravity and String Theory: (Super)-Gravities Beyond 4 Dimensions (J Zanelli); Introductory Lectures on String Theory and the AdS/CFT Correspondence (A Pankiewicz & S Theisen); Short Communications: Group Contractions and Its Consequences Upon Representations of Different Spatial Symmetry Groups (M Ayala-Sanchez & R W Haase); Phase Anomalies as Trace Anomalies in Chern-Simons Theory (A Cardona); Deligne Cohomology for Orbifolds, Discrete Torsion and B-Fields (E Lupercio & B Uribe).
£187.20
World Scientific Publishing Co Pte Ltd High-dimensional Manifold Topology - Proceedings
Book SynopsisThis work covers topics such as manifolds with positive scalar curvature, pseudo-isotopy spectrum and controlled theory, and reduction of the Novikov and Borel conjectures for aspherical complexes to aspherical manifolds.Table of ContentsA Foliated Squeezing Theorem for Geometric Modules (A Bartels et al.); Equivariant Cellular Homology and Its Applications (B Chorny); Remarks on a Conjecture of Gromov and Lawson (W Dwyer et al.); Chain Complex Invariants for Group Actions (L E Jones); The Ore Condition, Affiliated Operators, and the Lamplighter Group (P A Linnell et al.); The Surgery Exact Sequence Revisited (E K Pedersen); K-theory for Proper Smooth Actions of Totally Disconnected Groups (J Sauer); Geometric Chain Homotopy Equivalences between Novikov Complexes (D Schutz); and other papers.
£200.70
World Scientific Publishing Co Pte Ltd Hyperbolic Manifolds And Holomorphic Mappings: An
Book SynopsisThe first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.Trade Review"This book continues to serve as a fine introduction to hyperbolic complex analysis at a very elementary level." Zentralblatt MATH "A student with some background in complex differential geometry will find this to be an accessible, yet comprehensive, introduction to the subject." Mathematical ReviewsTable of Contents* The Schwarz Lemma and Its Generalizations * Volume Elements and the Schwarz Lemma * Distance and the Schwarz Lemma * Invariant Distances on Complex Manifolds * Holomorphic Mappings into Hyperbolic Manifolds * The Big Picard Theorem and Extension of Holomorphic Mappings * Generalization to Complex Spaces * Hyperbolic Manifolds and Minimal Models
£25.65
World Scientific Publishing Co Pte Ltd Universal Mandelbrot Set, The: Beginning Of The
Book SynopsisThis book is devoted to the structure of the Mandelbrot set — a remarkable and important feature of modern theoretical physics, related to chaos and fractals and simultaneously to analytical functions, Riemann surfaces, phase transitions and string theory. The Mandelbrot set is one of the bridges connecting the world of chaos and order.The authors restrict consideration to discrete dynamics of a single variable. This restriction preserves the most essential properties of the subject, but drastically simplifies computer simulations and the mathematical formalism.The coverage includes a basic description of the structure of the set of orbits and pre-orbits associated with any map of an analytic space into itself. A detailed study of the space of orbits (the algebraic Julia set) as a whole, together with related attributes, is provided. Also covered are: moduli space in the space of maps and the classification problem for analytic maps, the relation of the moduli space to the bifurcations (topology changes) of the set of orbits, a combinatorial description of the moduli space (Mandelbrot and secondary Mandelbrot sets) and the corresponding invariants (discriminants and resultants), and the construction of the universal discriminant of analytic functions in terms of series coefficients. The book concludes by solving the case of the quadratic map using the theory and methods discussed earlier.Table of ContentsNotions and Notation; Summary; Fragments of Theory; Map f(x) = X2 + c: From Standard Example to General Conclusions.
£88.20
World Scientific Publishing Co Pte Ltd Lecture Notes On Generalized Heegaard Splittings
Book SynopsisThis book is part of the series of three books arise from lectures organized by Hitoshi Murakami at RIMS, Kyoto University in the summer of 2001. The lecture series was aimed at a broad audience that included many graduate students. Its purpose lay in familiarizing the audience with the basics of 3-manifold theory and introducing some topics of current research. The first portion of the lecture series was devoted to standard topics in the theory of 3-manifolds. The middle portion was devoted to a brief study of Heegaard splittings and generalized Heegaard splittings.In the standard schematic diagram for generalized Heegaard splittings, Heegaard splittings are stacked on top of each other in a linear fashion. This can cause confusion in those cases in which generalized Heegaard splittings possess interesting connectivity properties. Fork complexes were invented in an effort to illuminate some of the more subtle issues arising in the study of generalized Heegaard splittings.Table of ContentsDefinitions and Examples of PL 3-Manifolds; Definitons and Examples of Heegaard Splittings; The Theorems of Reidemeister-Singer and Waldhausen; Generalized Heegaard Splittings and Fork Complexes;
£45.60
World Scientific Publishing Co Pte Ltd Introductory Topology: Exercises And Solutions
Book Synopsis'The book is well written, and there is a welcome breadth in the choice of topics. I think this book is a valuable resource. Students who meticulously work through all the problems in the book in an intelligent way, will surely gain considerable insight into the subject; teachers who don’t tell their students about it will find it a valuable source for exam questions.'The Mathematical GazetteThe book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.In the second edition, some significant changes have been made, other than the additional exercises. There are also additional proofs (as exercises) of many results in the old section 'What You Need To Know', which has been improved and renamed in the new edition as 'Essential Background'. Indeed, it has been considerably beefed up as it now includes more remarks and results for readers' convenience. The interesting sections 'True or False' and 'Tests' have remained as they were, apart from a very few changes.
£76.95
World Scientific Publishing Co Pte Ltd Introductory Topology: Exercises And Solutions
Book Synopsis'The book is well written, and there is a welcome breadth in the choice of topics. I think this book is a valuable resource. Students who meticulously work through all the problems in the book in an intelligent way, will surely gain considerable insight into the subject; teachers who don’t tell their students about it will find it a valuable source for exam questions.'The Mathematical GazetteThe book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.In the second edition, some significant changes have been made, other than the additional exercises. There are also additional proofs (as exercises) of many results in the old section 'What You Need To Know', which has been improved and renamed in the new edition as 'Essential Background'. Indeed, it has been considerably beefed up as it now includes more remarks and results for readers' convenience. The interesting sections 'True or False' and 'Tests' have remained as they were, apart from a very few changes.
£38.00
World Scientific Publishing Co Pte Ltd Geometry, Dynamics And Topology Of Foliations: A
Book SynopsisThe Geometric Theory of Foliations is one of the fields in Mathematics that gathers several distinct domains: Topology, Dynamical Systems, Differential Topology and Geometry, among others. Its great development has allowed a better comprehension of several phenomena of mathematical and physical nature. Our book contains material dating from the origins of the theory of foliations, from the original works of C Ehresmann and G Reeb, up till modern developments.In a suitable choice of topics we are able to cover material in a coherent way bringing the reader to the heart of recent results in the field. A number of theorems, nowadays considered to be classical, like the Reeb Stability Theorem, Haefliger's Theorem, and Novikov Compact leaf Theorem, are proved in the text. The stability theorem of Thurston and the compact leaf theorem of Plante are also thoroughly proved. Nevertheless, these notes are introductory and cover only a minor part of the basic aspects of the rich theory of foliations.
£76.95
World Scientific Publishing Co Pte Ltd Combinatorial And Toric Homotopy: Introductory
Book SynopsisThis volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning.The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics.The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students.
£133.20
World Scientific Publishing Co Pte Ltd Mereon Matrix, The: Everything Connected Through
Book SynopsisIn this richly illustrated book, the contributors describe the Mereon Matrix, its dynamic geometry and topology. Through the definition of eleven First Principles, it offers a new perspective on dynamic, whole and sustainable systems that may serve as a template information model. This template has been applied to a set of knowledge domains for verification purposes: pre-life-evolution, human molecular genetics and biological evolution, as well as one social application on classroom management.The importance of the book comes in the following ways:
£270.00
World Scientific Publishing Co Pte Ltd Topology And Physics
Book Synopsis'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems … The book explores many interesting and novel topics that lie at the intersection between gravity, quantum fields, condensed matter, physical cosmology and topology … A rich, well-organized, and comprehensive overview of remarkable and insightful connections between physics and topology is here made available to the physics reader.'Contemporary PhysicsSince its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably — resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences — finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.
£76.00
World Scientific Publishing Co Pte Ltd Topology And Physics
Book Synopsis'The book is an engaging and influential collection of significant contributions from an assembly of world expert leaders and pioneers from different fields, working at the interface between topology and physics or applications of topology to physical systems … The book explores many interesting and novel topics that lie at the intersection between gravity, quantum fields, condensed matter, physical cosmology and topology … A rich, well-organized, and comprehensive overview of remarkable and insightful connections between physics and topology is here made available to the physics reader.'Contemporary PhysicsSince its birth in Poincaré's seminal 1894 'Analysis Situs', topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably — resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences — finds its prominent role in physics. From Chern-Simons theory to topological quantum field theory, from knot invariants to Calabi-Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between 'Topology' and 'Physics'. Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.
£23.75
World Scientific Publishing Co Pte Ltd Classical Complex Analysis: A Geometric Approach
Book SynopsisClassical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 2 begins with analytic continuation. The Riemann mapping theorem is proved and used in solving Dirichlet's problem for an open disk and, hence, a class of general domains via Perron's method. Finally, proof of the uniformization theorem of Riemann surfaces is given.The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general.
£80.75
World Scientific Publishing Co Pte Ltd Virtual Knots: The State Of The Art
Book SynopsisThe book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory.In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams.Graph-links can be treated as “diagramless knot theory”: such “links” have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.Table of ContentsBasic Definitions and Notions; Virtual Knots and Three-Dimensional Topology; Quandles (Distributive Groupoids) in Virtual Knot Theory; The Jones Polynomial. Atoms; Khovanov Homology; Virtual Braids; Vassiliev's Invariants; Parity in Knot Theory. Free-Knots. Cobordisms; Theory of Graph-Links.
£131.25
World Scientific Publishing Co Pte Ltd Geometry, Topology And Dynamics Of Character
Book SynopsisThis volume is based on lectures given at the highly successful three-week Summer School on Geometry, Topology and Dynamics of Character Varieties held at the National University of Singapore's Institute for Mathematical Sciences in July 2010.Aimed at graduate students in the early stages of research, the edited and refereed articles comprise an excellent introduction to the subject of the program, much of which is otherwise available only in specialized texts. Topics include hyperbolic structures on surfaces and their degenerations, applications of ping-pong lemmas in various contexts, introductions to Lorenzian and complex hyperbolic geometry, and representation varieties of surface groups into PSL(2, ℝ) and other semi-simple Lie groups. This volume will serve as a useful portal to students and researchers in a vibrant and multi-faceted area of mathematics.Table of ContentsAn Invitation to Elementary Hyperbolic Geometry (Ying Zhang); Hyperbolic Structures on Surfaces (Javier Aramayona); Degenerations of Hyperbolic Structures on Surfaces (Chris Leininger); Ping-Pong Lemmas with Applications to Geometry and Topology (Thomas Michael Koberda); Creating Software for Visualizing Kleinian Groups (Yasushi Yamashita); Traces in Complex Hyperbolic Geometry (John Parker); Lorentzian Geometry (Todd Drumm); Connected Components of Representation Spaces (Frederic Palesi); Rigidity And Flexibility of Surface Groups in Semisimple Lie Groups (Inkang Kim); Abelian and Non-Abelian Cohomology (Eugene Xia).
£103.50
World Scientific Publishing Co Pte Ltd Topology With Applications: Topological Spaces
Book SynopsisThe principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.Table of ContentsBasic Framework; What is Topology?; Symmetric Proximity; Continuity and Proximal Continuity; Separation Axioms; Uniform Spaces, Filters and Nets; Compactness and Higher Separation Axioms; Initial and Final Structures, Embedding; Grills, Clusters, Bunches and Proximal Wallman Compactification; Extensions of Continuous Functions: Taimanov Theorem; Metrisation; Function Space Topologies; Hyperspace Topologies; Selected Topics: Uniformity and Metrisation.
£85.50
World Scientific Publishing Co Pte Ltd Homological Algebra: In Strongly Non-abelian
Book SynopsisWe propose here a study of ‘semiexact’ and ‘homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.This is a sequel of a book on ‘Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups’, published by the same Editor, but can be read independently of the latter.The previous book develops homological algebra in p-exact categories, i.e. exact categories in the sense of Puppe and Mitchell — a moderate generalisation of abelian categories that is nevertheless crucial for a theory of ‘coherence’ and ‘universal models’ of (even abelian) homological algebra. The main motivation of the present, much wider extension is that the exact sequences or spectral sequences produced by unstable homotopy theory cannot be dealt with in the previous framework.According to the present definitions, a semiexact category is a category equipped with an ideal of ‘null’ morphisms and provided with kernels and cokernels with respect to this ideal. A homological category satisfies some further conditions that allow the construction of subquotients and induced morphisms, in particular the homology of a chain complex or the spectral sequence of an exact couple.Extending abelian categories, and also the p-exact ones, these notions include the usual domains of homology and homotopy theories, e.g. the category of ‘pairs’ of topological spaces or groups; they also include their codomains, since the sequences of homotopy ‘objects’ for a pair of pointed spaces or a fibration can be viewed as exact sequences in a homological category, whose objects are actions of groups on pointed sets.Table of ContentsIntroduction; Semiexact categories; Homological Categories; Subquotients, Homology and Exact Couples; Satellites; Universal Constructions; Applications to Algebraic Topology; Homological Theories and Biuniversal Models; Appendix A. Some Points of Category Theory.
£95.40
World Scientific Publishing Co Pte Ltd Theta Functions And Knots
Book SynopsisThis book presents the relationship between classical theta functions and knots. It is based on a novel idea of Răzvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology.Theta Functions and Knots can be read in two perspectives. Readers with an interest in theta functions or knot theory can learn how the two are related. Those interested in Chern-Simons theory will find here an introduction using the simplest case, that of abelian Chern-Simons theory. Moreover, the construction of abelian Chern-Simons theory is based entirely on quantum mechanics and not on quantum field theory as it is usually done.Both the theory of theta functions and low dimensional topology are presented in detail, in order to underline how deep the connection between these two fundamental mathematical subjects is. Hence the book is self-contained with a unified presentation. It is suitable for an advanced graduate course, as well as for self-study.Table of ContentsSome Historical Facts; A Quantum Mechanical Prototype; Surfaces and Curves; The Theta Functions Associated to a Riemann Surface; From Theta Functions to Knots; Some Results About 3- and 4-Dimensional Manifolds; The Discrete Fourier Transform and Topological Quantum Field Theory; Theta Functions and Quantum Groups; An Epilogue - Abelian Chern - Simons Theory.
£135.00
World Scientific Publishing Co Pte Ltd Harmonic And Spectral Analysis
Book SynopsisThis book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical harmonic analysis together with the recent developments in spectral analysis and synthesis.Table of ContentsDuality of Finite Abelian Groups; Harmonic Analysis on Finite Abelian Groups; Invariant Means on Abelian Groups; Duality of Discrete and Compact Abelian Groups; Duality of Elementary Abelian Groups; Harmonic Analysis on Compact Abelian Groups; Duality of Locally Compact Abelian Groups; Harmonic Analysis on Locally Compact Abelian Groups; Haar Integral on Locally Compact Abelian Groups; Spectral Analysis on Abelian Groups; Spectral Synthesis on Abelian Groups; Spectral Analysis and Synthesis on Varieties; Noncommutative Spectral Synthesis.
£76.95
World Scientific Publishing Co Pte Ltd Convergence Foundations Of Topology
Book SynopsisThis textbook is an alternative to a classical introductory book in point-set topology. The approach, however, is radically different from the classical one. It is based on convergence rather than on open and closed sets. Convergence of filters is a natural generalization of the basic and well-known concept of convergence of sequences, so that convergence theory is more natural and intuitive to many, perhaps most, students than classical topology. On the other hand, the framework of convergence is easier, more powerful and far-reaching which highlights a need for a theory of convergence in various branches of analysis.Convergence theory for filters is gradually introduced and systematically developed. Topological spaces are presented as a special subclass of convergence spaces of particular interest, but a large part of the material usually developed in a topology textbook is treated in the larger realm of convergence spaces.Table of ContentsIntroduction; Convergences; Pretopologies; Separation; Pseudotopologies; Compactness; Completeness; Extensions; Structural Aspects; Spaces of Maps; Connectedness; Metrizability and Complete Metrizability.
£108.00
World Scientific Publishing Co Pte Ltd Convergence Foundations Of Topology
Book SynopsisThis textbook is an alternative to a classical introductory book in point-set topology. The approach, however, is radically different from the classical one. It is based on convergence rather than on open and closed sets. Convergence of filters is a natural generalization of the basic and well-known concept of convergence of sequences, so that convergence theory is more natural and intuitive to many, perhaps most, students than classical topology. On the other hand, the framework of convergence is easier, more powerful and far-reaching which highlights a need for a theory of convergence in various branches of analysis.Convergence theory for filters is gradually introduced and systematically developed. Topological spaces are presented as a special subclass of convergence spaces of particular interest, but a large part of the material usually developed in a topology textbook is treated in the larger realm of convergence spaces.Table of ContentsIntroduction; Convergences; Pretopologies; Separation; Pseudotopologies; Compactness; Completeness; Extensions; Structural Aspects; Spaces of Maps; Connectedness; Metrizability and Complete Metrizability.
£61.75
World Scientific Publishing Co Pte Ltd Introductory Topology: Exercises And Solutions
Book SynopsisThe book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.Table of ContentsExercises and Solutions: General Notions: Sets, Functions et al.; Metric Spaces; Topological Spaces; Continuity and Convergence; Compact Spaces; Connected Spaces; Complete Metric Spaces; Function Spaces;
£28.50
World Scientific Publishing Co Pte Ltd Topics On Real And Complex Singularities
Book SynopsisA phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized. For example, the Hamiltonian mechanics, soapy films, size of an atom, business management, etc. In mathematics, a point where a given function attains an extreme value is called a critical point, or a singular point. The purpose of singularity theory is to explore the properties of singular points of functions and mappings.This is a volume on the proceedings of the fourth Japanese-Australian Workshop on Real and Complex Singularities held in Kobe, Japan. It consists of 11 original articles on singularities. Readers will be introduced to some important new notions for characterizations of singularities and several interesting results are delivered. In addition, current approaches to classical topics and state-of-the-art effective computational methods of invariants of singularities are also presented. This volume will be useful not only to the singularity theory specialists but also to general mathematicians.
£85.50
World Scientific Publishing Co Pte Ltd New Ideas In Low Dimensional Topology
Book SynopsisThis book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.Table of ContentsCasson-Type Invariants from the Seiberg-Witten Equations (D Ruberman and N Saveliev); Dirac Operators in Gauge Theory (A Haydys); How to Fold a Manifold (J Scott Carter and S Kamada); Generalised Biquandles for Generalised Knot Theories (R Fenn); Graph-Links: The State of the Art (D P Ilyutko, V O Manturov, I M Nikonov); Lectures on Knot Homology and Quantum Curves (S Gukov and I Saberi); Reidemeister / Roseman-type Moves to Embedded Foams in 4-dimensional Space (J Scott Carter); Virtual Knot Cobordism (L H Kauffman); Mutant Knots (H R Morton); Ordering Knot Groups (D Rolfsen); A Survey of Heegaard Floer Homology (A Juhasz); On the Framization of Knot Algebras (J Juyumaya & S Lambropoulou) and other papers;
£153.00
World Scientific Publishing Co Pte Ltd Many-body Physics, Topology And Geometry
Book SynopsisThe book explains concepts and ideas of mathematics and physics that are relevant for advanced students and researchers of condensed matter physics. With this aim, a brief intuitive introduction to many-body theory is given as a powerful qualitative tool for understanding complex systems. The important emergent concept of a quasiparticle is then introduced as a way to reduce a many-body problem to a single particle quantum problem. Examples of quasiparticles in graphene, superconductors, superfluids and in a topological insulator on a superconductor are discussed.The mathematical idea of self-adjoint extension, which allows short distance information to be included in an effective long distance theory through boundary conditions, is introduced through simple examples and then applied extensively to analyse and predict new physical consequences for graphene.The mathematical discipline of topology is introduced in an intuitive way and is then combined with the methods of differential geometry to show how the emergence of gapless states can be understood. Practical ways of carrying out topological calculations are described.Table of ContentsOverview; many-Body Theory; Topology and Geometry; Boundary Conditions and Self-Adjoint Extensions; Electronic Properties of Graphene;
£55.10
World Scientific Publishing Co Pte Ltd Representing 3-manifolds By Filling Dehn Surfaces
Book SynopsisThis book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.
£99.00
World Scientific Publishing Co Pte Ltd Piecewise Linear Structures On Topological
Book SynopsisThe study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s-early 1970s in a complete classification in the work of Kirby and Siebenmann. It is this classification that we discuss in this book, including the celebrated Hauptvermutung and Triangulation Conjecture.The goal of this book is to provide a readable and well-organized exposition of the subject, which would be suitable for advanced graduate students in topology. An exposition like this is currently lacking.Table of ContentsArchitecture of the Proof; Normal Invariant; Applications and Consequences of Main Theorem;
£74.10
Springer Advances in Topology Dynamical Systems and
Book SynopsisChapter 1 Closure Functions Induced by * and psi Operators.- Chapter 2 PNDP Manifolds.- Chapter 3 A Unified Study of Normal Spaces.
£116.99
Springer Monopole Maps and L cohomology
Book SynopsisChapter 1 Introduction.- Chapter 2 A glimpse of progress of di?erential topology.- Chapter 3 Spin geometry.- Chapter 4 Seiberg–Witten theory.- Chapter 5 Bauer–Furuta theory.- Chapter 6 ??^?? cohomology.- Chapter 7 ??^2-Betti number and von Neumann trace.- Chapter 8 Aspherical 10/8 -inequality and Singer’s conjecture.- Solutions.- References.- Index.
£125.99
World Scientific Publishing Co Pte Ltd Metric Space Topology Examples Exercises And Solutions
£52.25
World Scientific Publishing Co Pte Ltd Pointset Topology With Topics Basic General
Book Synopsis
£76.00
Springer Verlag, Singapore A Comprehensive Textbook on Metric Spaces
Book SynopsisThis textbook provides a comprehensive course in metric spaces. Presenting a smooth takeoff from basic real analysis to metric spaces, every chapter of the book presents a single concept, which is further unfolded and elaborated through related sections and subsections. Apart from a unique new presentation and being a comprehensive textbook on metric spaces, it contains some special concepts and new proofs of old results, which are not available in any other book on metric spaces. It has individual chapters on homeomorphisms and the Cantor set. This book is almost self-contained and has an abundance of examples, exercises, references and remarks about the history of basic notions and results. Every chapter of this book includes brief hints and solutions to selected exercises. It is targeted to serve as a textbook for advanced undergraduate and beginning graduate students of mathematics. Table of ContentsReal Analysis.- Metric Spaces.- Topology.- Completeness.- Compactness.- Connectedness.- Cardinality.- Denseness.-Homeomorphisms.- The Cantor Set.- Appendixes.- Bibliography.- Index.
£62.99
