Topology Books
Taylor & Francis Ltd Introduction to Lorentz Geometry
Book SynopsisLorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style wTable of Contents1. Welcome to Lorentz-Minkowski Space. 1.1. Pseudo–Euclidean Spaces. 1.2. Subspaces of Rᵑᵥ. 1.3. Contextualization in Special Relativity. 1.4. Isometries in Rᵑᵥ. 1.5. Investigating O1(2, R) And O1(3, R). 1.6 Cross Product in Rᵑᵥ. 2. Local Theory of Curves. 2.1. Parametrized Curves in Rᵑᵥ. 2.2. Curves in the Plane. 2.3. Curves in Space. 3. Surfaces in Space. 3.1. Basic Topology of Surfaces. 3.2. Casual type of Surfaces, First Fundamental Form. 3.3. Second Fundamental Form and Curvatures. 3.4. The Diagonalization Problem. 3.5. Curves in Surface. 3.6. Geodesics, Variational Methods and Energy. 3.7. The Fundamental Theorem of Surfaces. 4. Abstract Surfaces and Further Topics. 4.1. Pseudo-Riemannian Metrics. 4.2. Riemann’s Classification Theorem. 4.3. Split-Complex Numbers and Critical Surfaces. 4.4 Digression: Completeness and Causality
£36.99
Taylor & Francis Ltd FourDimensional Manifolds and Projective Structure
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£99.75
Taylor & Francis Ltd Differential Geometry and Its Visualization
Book SynopsisDifferential Geometry and Its Visualization is suitable for graduate level courses in differential geometry, serving both students and teachers. It can also be used as a supplementary reference for research in mathematics and the natural and engineering sciences.Differential geometry is the study of geometric objects and their properties using the methods of mathematical analysis. The classical theory of curves and surfaces in three-dimensional Euclidean space is presented in the first three chapters. The abstract and modern topics of tensor algebra, Riemannian spaces and tensor analysis are studied in the last two chapters. A great number of illustrating examples, visualizations and genuine figures created by the authors' own software are included to support the understanding of the presented concepts and results, and to develop an adequate perception of the shapes of geometric objects, their properties and the relations between them.FeatuTable of Contents1. Curves in Three–dimensional Euclidean Space. 1.1. Points and Vectors. 1.2. Vector–valued Functions of a Real Variable. 1.3. The General Concept of Curves. 1.4. Some Examples of Planar Curves. 1.5. The Arc Length of a Curve. 1.6. The Vectors of the Trihedron of a Curve. 1.7. Frenet’s Formulae. 1.8. The Geometric Significance of Curvature and Torsion. 1.9. Osculating Circles and Spheres. 1.10. Involutes and Evolutes. 1.11. The Fundamental Theorem of Curves. 1.12. Lines of Constant Slope. 1.13. Spherical Images of a Curve. 2. Surfaces in Three–dimensional Euclidean Space. 2.1. Surfaces and Curves on Surfaces. 2.2. The Tangent Planes and Normal Vectors of a Surface. 2.3. The Arc Length, Angles and Gauss’s First Fundamental Coefficients. 2.4. the Curvature of Curves on Surfaces, Geodesic and Normal Curvature. 2.5. The Normal, Principal, Gaussian and Mean Curvature. 2.6. The Shape of a Surface in the Neighbourhood of a Point. 2.7. Dupin’s Indicatrix. 2.8. Lines of Curvature and Asymptotic Lines. 2.9. Triple Orthogonal Systems. 2.10. the Weingarten Equations. 3. The Intrinsic Geometry of Surfaces. 3.1. the Christoffel Symbols. 3.2. Geodesic Lines. 3.3. Geodesic Lines on Surfaces with Orthogonal Parameters. 3.4. Geodesic Lines on Surfaces of Revolution. 3.5. the Minimum Property of Geodesic Lines. 3.6. Orthogonal and Geodesic Parameters. 3.7. Levi–civitá Parallelism. 3.8. Theorema Egregium. 3.9. Maps Between Surfaces. 3.10. the Gauss–bonnet Theorem. 3.11. Minimal Surfaces. 4. Tensor Algebra and Riemannian Geometry. 4.1. Differentiable Manifolds. 4.2. Transformation of Bases. 4.3. Linear Functionals and Dual Spaces. 4.4. Tensors of Second Order. 4.5. Symmetric Bilinear Forms and Inner Products. 4.6. Tensors of Arbitary Order. 4.7. Symmetric and Anti–symmetric Tensors. 4.8. Riemann Spaces. 4.9. the Christoffel Symbols. 5. Tensor Analysis. 5.1. Covariant Differentiation. 5.2. the Covariant Derivative of an (R, S)–tensor. 5.3. the Interchange of Order for Covariant Differentiation and Ricci’s Identity. 5.4. Bianchi’s Identities for the Covariant Derivative of the Tensors of Curvature. 5.5. Beltrami’s Differentiators. 5.6. a Geometric Meaning of the Covariant Differentiation, the Levi–civitá Parallelism. 5.7. The Fundamental Theorem for Surfaces. 5.8. A Geometric Meaning of the Riemann Tensor of Curvature. 5.9. Spaces With Vanishing Tensor of Curvature. 5.10. An Extension of Frenet’s Formulae. 5.11. Riemann Normal Coordinates and the Curvature of Spaces.
£80.74
Cambridge University Press Topology for Computing 16 Cambridge Monographs on Applied and Computational Mathematics Series Number 16
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£47.49
Cambridge University Press Real and Complex Singularities
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£62.54
Cambridge University Press Typical Dynamics of Volume Preserving Homeomorphisms 139 Cambridge Tracts in Mathematics Series Number 139
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£36.87
Cambridge University Press Electromagnetic Theory and Computation A Topological Approach 48 Mathematical Sciences Research Institute Publications Series Number 48
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£49.39
Cambridge University Press Deterministic Observation Theory and Applications
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£35.14
Cambridge University Press Topology of Stratified Spaces
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£133.95
Cambridge University Press Differentiable Germs and Catastrophes 17 London Mathematical Society Lecture Note Series Series Number 17
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£45.16
Cambridge University Press Fixed Point Theorems with Applications to Economics and Game Theory
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£44.64
Cambridge University Press Complex Polynomials 75 Cambridge Studies in Advanced Mathematics Series Number 75
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£133.95
Cambridge University Press Geometry of Sporadic Groups Volume 1 Petersen and Tilde Geometries Encyclopedia of Mathematics and its Applications Series Number 76
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£122.55
Cambridge University Press LMS 197 Two Dimensional Homotopy London Mathematical Society Lecture Note Series Series Number 197
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£61.71
Cambridge University Press Complexity Knots Colourings and Countings 186 London Mathematical Society Lecture Note Series Series Number 186
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£57.57
Cambridge University Press Combinatorial and Geometric Group Theory Edinburgh 1993 Proceedings of ICMS Workshop Held at HeriotWatt University 23 March to 8 April 1993 204 Lecture Note Series Series Number 204
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£65.86
Cambridge University Press thealgebraiccharacterizationofgeometric4manifolds
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£55.09
Cambridge University Press Geometry and Integrability 295 London Mathematical Society Lecture Note Series Series Number 295
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£69.99
Cambridge University Press The Homotopy Category of Simply Connected 4Manifolds 297 London Mathematical Society Lecture Note Series Series Number 297
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£50.99
Cambridge University Press The Changing Shape of Geometry Celebrating a Century of Geometry and Geometry Teaching Maa Spectrum Series
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£47.49
Cambridge University Press Stable Modules and the D2Problem 301 London Mathematical Society Lecture Note Series Series Number 301
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£61.71
Cambridge University Press Frobenius Algebras and 2D Topological Quantum Field Theories 59 London Mathematical Society Student Texts Series Number 59
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£52.24
Cambridge University Press Topology Geometry and Quantum Field Theory Proceedings of the 2002 Oxford Symposium in Honour of the 60th Birthday of Graeme Segal 308 London Lecture Note Series Series Number 308
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£105.60
Cambridge University Press A Users Guide to Spectral Sequences 58 Cambridge Studies in Advanced Mathematics Series Number 58
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£111.15
Cambridge University Press Topology via Logic
Book SynopsisThis is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.Table of Contents1. Introduction; 2. Affirmative and refutative assertions; 3. Frames; 4. Frames as algebras; 5. Topology: the definitions; 6. New topologies for old; 7. Point logic; 8. Compactness; 9. Spectral algebraic locales; 10. Domain theory; 11. Power domains; 12. Spectra of rings; Bibliography.
£45.59
Cambridge University Press Typical Dynamics of Volume Preserving Homeomorphisms 139 Cambridge Tracts in Mathematics Series Number 139
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£105.45
Cambridge University Press LMS 248 Tame Topology ominimal London Mathematical Society Lecture Note Series Series Number 248
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£61.99
Cambridge University Press Hausdorff Measures Cambridge Mathematical Library
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£53.19
Cambridge University Press Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces 269 London Mathematical Society Lecture Note Series Series Number 269
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£65.99
Cambridge University Press When Topology Meets Chemistry
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£95.95
Cambridge University Press When Topology Meets Chemistry
Book SynopsisIn this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, and the role these play in understanding molecular structures. All the relevant background is provided. For advanced undergraduate mathematics students, and researchers in chemistry and biology.Trade Review'If you are a chemist … looking for applications of low dimensional topology in the natural sciences, this is a book you should own … serves as an excellent introduction to the field for a topologist looking for interesting applications of topology in science. The book is well produced with many useful diagrams and with exercises that range from easy to intriguing. This book is definitely on my 'buy list'.' Stuart Whittington, SIAM ReviewTable of Contents1. Stereochemical topology; 2. Detecting chirality; 3. Chiral moebius ladders and related molecular graphs; 4. Different types of chirality and achirality; 5. Embeddings of complete graphs in 3-space; 6. Rigid and non-rigid symmetries of graphs in 3-space; 7. Topology of DNA.
£33.24
Cambridge University Press Handbook of Tilting Theory 332 London Mathematical Society Lecture Note Series Series Number 332
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£82.41
Cambridge University Press Noncommutative Localization in Algebra and Topology 330 London Mathematical Society Lecture Note Series Series Number 330
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£61.71
Cambridge University Press Lectures on the Ricci Flow 325 London Mathematical Society Lecture Note Series Series Number 325
Book SynopsisHamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003.Trade Review"... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read." Peng Lu, Mathematical ReviewsTable of Contents1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.
£55.91
Cambridge University Press Characters and Automorphism Groups of Compact Riemann Surfaces 280 London Mathematical Society Lecture Note Series Series Number 280
Book SynopsisUsing modern methods from computational group theory and representation theory, this book addresses a classical topic in the theory of complex functions. It is suitable for graduate students and researchers.Trade Review'… by bringing together a number of very effective techniques, and by presenting a mass of specific evidence, Breuer has done the mathematical community a considerable service … the presentation of the material is excellent, with attractive layout … a valuable addition to the literature, which should be essential reading for anyone interested in the connections between Riemann surfaces and finite groups.' G. Jones, Proceedings of the Edinburgh Mathematical SocietyTable of ContentsPreface; Notation; 1. Compact Riemann surfaces; 2. Group characters; 3. Automorphisms of compact Riemann surfaces; 4. Generation of groups; 5. Classification for small genus; 6. Classification for fixed group: real characters; 7. Classification for fixed group: nonreal irrationalities; Appendix A. Abelian inariants; Appendix B. Irreducible characters; Appendix C. Maillet's determinant; Bibliography; Index.
£57.57
Cambridge University Press An Algebraic Introduction to KTheory 87 Encyclopedia of Mathematics and its Applications Series Number 87
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£152.95
Cambridge University Press Topics in Topological Graph Theory 129 Encyclopedia of Mathematics and its Applications Series Number 128
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£122.55
Cambridge University Press Deterministic Observation Theory and Applications
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£104.50
Cambridge University Press An Introduction to Invariants and Moduli 81 Cambridge Studies in Advanced Mathematics Series Number 81
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£130.15
Cambridge University Press Frobenius Manifolds and Moduli Spaces for Singularities 151 Cambridge Tracts in Mathematics Series Number 151
Book SynopsisThe relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity theory, quantum cohomology, mirror symmetry, symplectic geometry and integrable systems. The first part of the book explains the theory of manifolds with a multiplication on the tangent bundle. The second presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will find here a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.Trade Review'… a nice introduction to the theory of Frobenius manifolds …' Zentralblatt für Mathematik'The book under review gives a very detailed analysis of the category of F-manifolds … the book is clean, rigorous and readable. the researchers in the areas of singularity theory, complex geometry, integrable systems, quantum cohomology, mirror symmetry and sympathetic geometry will find in this book a lot of useful information which has never been given in such detail before.' Proceedings of the Edinburgh Mathematical Society'… one can say this book is a must for workers in the field of singularity theory.' Duco van Straten, Department of Mathematics, University of MainzTable of ContentsPart I. Multiplication on the Tangent Bundle: 1. Introduction to part 1; 2. Definition and first properties of F-manifolds; 3. Massive F-manifolds and Lagrange maps; 4. Discriminants and modality of F-manifolds; 5. Singularities and Coxeter groups; Part II. Frobenius Manifolds, Gauss-Manin Connections, and Moduli Spaces for Hypersurface Singularities: 6. Introduction to part 2; 7. Connections on the punctured plane; 8. Meromorphic connections; 9. Frobenius manifolds ad second structure connections; 10. Gauss-Manin connections for hypersurface singularities; 11. Frobenius manifolds for hypersurface singularities; 12. ∴μυ-constant stratum; 13. Moduli spaces for singularities; 14. Variance of the spectral numbers.
£105.45
Cambridge University Press Abstract Regular Polytopes 92 Encyclopedia of Mathematics and its Applications Series Number 92
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£151.05
Cambridge University Press The Changing Shape of Geometry Celebrating a Century of Geometry and Geometry Teaching Maa Spectrum Series
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£111.00
Cambridge University Press The Life of Bach Musical Lives
Book SynopsisArising from a summer school course, this book develops the modern theory of rational varieties at a level that will particularly suit graduate students. The authors have written a state-of-the-art treatment with numerous exercises and solutions to help students reach the stage where they can begin to tackle contemporary research.Trade Review'… a beautiful and ample introduction to the interesting topic of rational and 'nearly rational' varieties and it will be a valuable reference for a wide audience.' Zentralblatt MATHTable of ContentsIntroduction; 1. Examples of rational varieties; 2. Cubic surfaces; 3. Rational surfaces; 4. Nonrationality and reduction modulo p; 5. The Noether-Fano method; 6. Singularities of pairs; 7. Solutions to exercises.
£105.45
Cambridge University Press Frobenius Algebras and 2D Topological Quantum Field Theories London Mathematical Society Student Texts Book 59
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£133.95
Cambridge University Press Topology for Computing 16 Cambridge Monographs on Applied and Computational Mathematics Series Number 16
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£103.11
Cambridge University Press Topological Solitons
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£155.80
Cambridge University Press The CubeA Window to Convex and Discrete Geometry
Book SynopsisThis tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them.Trade Review"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended." -- ChoiceTable of ContentsPreface; Basic notation; 0. Introduction; 1. Cross sections; 2. Projections; 3. Inscribed simplices; 4. Triangulations; 5. 0/1 polytopes; 6. Minkowski's conjecture; 7. Furtwangler's conjecture; 8. Keller's conjecture; Bibliography; Index.
£105.45
Cambridge University Press An Introduction to Contact Topology 109 Cambridge
Book SynopsisThis text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.Trade Review'… a fundamental monograph … can be strongly recommended for graduate students and is indispensable for specialists in the field.' EMS NewsletterTable of ContentsForeword; 1. Facets of Contact Geometry; 2. Contact Manifolds; 3. Knots in Contact 3-Manifolds; 4. Contact Structures on 3-Manifolds; 5. Symplectic Fillings and Convexity; 6. Contact Surgery; 7. Further Constructions of Contact Manifolds; 8. Contact Structures on 5-Manifolds; Appendix A. The generalised Poincaré lemma; Appendix B. Time-dependent vector fields; References; Notation Index; Author Index; Subject Index.
£77.89