An Introduction to Differential Geometry and Topology in Mathematical Physics

by Rong, Wang; Yue, Cheng

• ISBN13: 9789810235598
• ISBN10: 9810235593
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Presents an outline of the classical results and the most recent developments of differential geometry and topology, especially those important developments which are closely related to the new discoveries in the field of theoretical physics.

Table of Contents

Acknowledgments
Preface
Differential Manifolds
Preliminary Knowledge and Definitions	p. 1
Properties and Operations of Tangent Vectors and Cotangent Vectors	p. 18
Curvature Tensors, Torsion Tensors, Covariant Differentials and Adjoint Exterior Differentials	p. 34
Riemannian Geometry	p. 50
Complex Manifold	p. 68
Global Topological Properties
Homotopy Equivalence and Homotopy Groups of Manifolds	p. 84
Homology and de Rham Cohomology	p. 98
Fibre Bundles and their Topological Structures	p. 115
Connections and Curvatures on Fibre Bundles	p. 130
Characteristic Classes of Fibre Bundles	p. 146
Index Theorems and 4-manifolds
Index Theorems for Manifolds without Boundary	p. 162
Essential Features of 4-Manifolds	p. 182
References	p. 207
Index	p. 208
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