Algebraic topology Books
World Scientific Publishing Co Pte Ltd Knots And Physics (Fourth Edition)
Book SynopsisThis invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.Table of ContentsPhysical Knots; States and the Bracket Polynomial; The Jones Polynomial and Its Generalizations; Braids and the Jones Polynomial; Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q; Yang - Baxter Models for Specializations of the Homfly Polynomial; Knot-Crystals - Classical Knot Theory in a Modern Guise; The Kauffman Polynomial; Three Manifold Invariants from the Jones Polynomial; Integral Heuristics and Witten's Invariants; The Chromatic Polynomial; The Potts Model and the Dichromatic Polynomial; The Penrose Theory of Spin Networks; Knots and Strings - Knotted Strings; DNA and Quantum Field Theory; Knots in Dynamical Systems - The Lorenz Attractor; and selected papers.
£72.20
World Scientific Publishing Co Pte Ltd Topological Library - Part 3: Spectral Sequences
Book SynopsisThe final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.”Table of ContentsSingular Homology of Fiber Spaces (J-P Serre); Homotopy Groups and Classes of Abelian Groups (J-P Serre); Cohomology Modulo 2 of Eilenberg - MacLane Complexes (J-P Serre); On Cohomology of Principal Fiber Bundles and Homogeneous Spaces of Compact Lie Groups (A Borel); Cohomology Mod 2 of Some Homogeneous Spaces (A Borel); The Steenrod Algebra and Its Dual (J Milnor); On the Structure and Applications of the Steenrod Algebra (J F Adams); Vector Bundles and Homogeneous Spaces (M F Atyah and F Hirzebruch); The Methods of Algebraic Topology from Viewpoint of Cobordism Theory (S P Novikov).
£166.50
World Scientific Publishing Co Pte Ltd Advances In The Homotopy Analysis Method
Book SynopsisUnlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the HAM from all other analytic approximation methods. In addition, the HAM can be applied to solve some challenging problems with high nonlinearity.This book, edited by the pioneer and founder of the HAM, describes the current advances of this powerful analytic approximation method for highly nonlinear problems. Coming from different countries and fields of research, the authors of each chapter are top experts in the HAM and its applications.Table of ContentsA Short Review of Homotopy Analysis Method: Change and Challenge; Predictor Homotopy Analysis Method; Spectral Homotopy Analysis Method; Stability of Auxiliary Linear Operator and Convergence - Control Parameter; On the Convergence of the Homotopy Analysis Method; Homotopy Analysis Method for Some Boundary Layer Flows of Nanofluids; Homotopy Analysis Method for Fractional Swift - Hohenberg Equation; Homotopy Analysis Method-based Package NOPH for Periodic Oscillations; Homotopy Analysis Method-based Package BVPh 2.0 for Nonlinear BVPs.
£121.50
World Scientific Publishing Co Pte Ltd New Topological Invariants For Real- And
Book SynopsisThis book is about new topological invariants of real- and angle-valued maps inspired by Morse-Novikov theory, a chapter of topology, which has recently raised interest outside of mathematics; for example, in data analysis, shape recognition, computer science and physics. They are the backbone of what the author proposes as a computational alternative to Morse-Novikov theory, referred to in this book as AMN-theory.These invariants are on one side analogues of rest points, instantons and closed trajectories of vector fields and on the other side, refine basic topological invariants like homology and monodromy. They are associated to tame maps, considerably more general than Morse maps, that are defined on spaces which are considerably more general than manifolds. They are computable by computer implementable algorithms and have strong robustness properties. They relate the dynamics of flows that admit the map as 'Lyapunov map' to the topology of the underlying space, in a similar manner as Morse-Novikov theory does.Table of ContentsPreliminary Material; Homology/Betti Numbers; Graph Representations; Alexander Function; Invariants for a (Weakly) Tame Map; The Main Results (So Far); Mathematical Implications; Relation with More Sophisticated Mathematics (Constructive Sheafs);
£65.55
World Scientific Publishing Co Pte Ltd Morse Theory: Smooth And Discrete
Book SynopsisMorse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the book a valuable resource for students and professionals working in topology and discrete mathematics. With a strong focus on examples, the text is suitable for advanced undergraduates or beginning graduate students.Table of ContentsSmooth Morse Theory: First Steps (Surfaces, Critical Points); Fundamental Results (Morse Lemma, Existence, Gradient-Like Vector Fields); Topological Consequences (Homotopy Type, Morse Inequalities); Discrete Morse Theory: First Steps (Definitions and Examples); Fundamental Results (Existence, Gradients); Topological Consequences (Homotopy Type, Collapses); Algorithms (Constructing Discrete Morse Functions); Appendices: Smooth Manifolds; Simplicial Complexes;
£51.30
World Scientific Publishing Co Pte Ltd Rational Homotopy Theory Ii
Book SynopsisThis research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions.This monograph is a sequel to the book Rational Homotopy Theory [RHT], published by Springer in 2001, but is self-contained except only that some results from [RHT] are simply quoted without proof.Table of ContentsSullivan Model and Rationalization of a Non-Simply Connected Space; Homotopy Lie Algebra of a Space and Fundamental Group of the Rationalization, Model of a Fibration; Holonomy Operation in a Fibration; Malcev Completion of a Group and Examples; Lusternik-Schnirelmann Category; Depth of a Sullivan Lie Algebra; Growth of Rational Homotopy Groups; Structure of Rational Homotopy Lie Algebras; Weighted Lie Algebras;
£124.20
World Scientific Publishing Co Pte Ltd Etale Cohomology Theory (Revised Edition)
Book SynopsisEtale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ℓ-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.Table of ContentsDescent Theory; Etale Morphisms and Smooth Morphisms; Etale Fundamental Groups; Group Cohomology and Galois Cohomology; Etale Cohomology; Derived Categories and Derived Functors; Base Change Theorems; Duality; Finiteness Theorems; -Adic Cohomology;
£180.00
World Scientific Publishing Co Pte Ltd Lecture Notes On Knot Invariants
Book SynopsisThe volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.
£58.90
World Scientific Publishing Co Pte Ltd Lecture Notes On Knot Invariants
Book SynopsisThe volume is focused on the basic calculation skills of various knot invariants defined from topology and geometry. It presents the detailed Hecke algebra and braid representation to illustrate the original Jones polynomial (rather than the algebraic formal definition many other books and research articles use) and provides self-contained proofs of the Tait conjecture (one of the big achievements from the Jones invariant). It also presents explicit computations to the Casson-Lin invariant via braid representations.With the approach of an explicit computational point of view on knot invariants, this user-friendly volume will benefit readers to easily understand low-dimensional topology from examples and computations, rather than only knowing terminologies and theorems.
£30.40
Springer Lefschetz Properties
Book SynopsisSurvey articles about specific topics.- Jordan types and relation with WLP/SLP.- Unexpected objects, connections with Lefschetz properties and special sets of points.- Combinatorial aspects.- Working group on Perazzo hypersurfaces Hilbert functions, WLP, Jordan types.
£134.99
