This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8-10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.
Author(s): Bo-Yu Hou, Bo-Yuan Hou
Series: Advanced Series On Theoretical Physical Science 6
Publisher: World Scientific Publishing Co Pte Ltd
Year: 1997
Language: English
Commentary: ocrmypdf optimized
Pages: 560
Contents
Preface
Chapter 1 Differentiable Manifolds and Differential Forms
Chapter 2 Transformation of Manifold, Manifolds with Given Vector Fields and Lie Group Manifold
Chapter 3 Affine Connection and Covariant Differentiation
Chapter 4 Riemannian Manifold
Chapter 5 Symplectic Manifold and Contact Manifold
Chapter 6 Complex Manifolds
Chapter 9 Differential Geometry of Fibre Bundle, Yang-Mills Gauge Theory
Chapter 10 Characteristic Classes
Chapter 11 The Atiyah-Singer Index Theorem
Chapter 12 Index Theorem on Manifold with Boundary and on Open Infinite Manifold
Chapter 14 Noncommutative Geometry, Quantum Group, and (/-deformation of Chern-Characters
Appendix A Simple Introduction to Set Theory
Appendix B Preliminary Topology
Appendix C Some Basic Algebraic Structures
Appendix D Homomorphism of Algebraic Structure and Tensor Algebra
Appendix E Exact Sequence of Homomorphism
Appendix F Abelian Group
Appendix G Stokes' Theorem
Appendix H Quarternion and Milnor Exotic Spheres
Appendix I Generalized Kronecker 5 notation
Appendix J n-dimensional Sphere
Appendix K 5(7(2) Group Manifold
Appendix L S2 Manifold and Hopf Maps
Appendix M Clifford Algebra, Spin Group and its Representations
Appendix N Good Cover and the Nerve of a Cover. Cech Cohomology
Appendix O Symmetric Trace
Appendix P Cohomology with Compact Support and Cohomology on Fibre Bundle, Thorn Class
Appendix Q K-theory, Topological Invariance of Elliptic Operator
Appendix R Cohomology of Lie group and Lie algebra
Appendix S
Index
