Introduction to Smooth Manifolds /
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research-smooth structures, tangent vectors and covectors, vector bundles, immersed and em...
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| Format: | Book |
| Language: | English |
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New York, NY :
Springer New York : Imprint: Springer,
2012
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| Edition: | Second edition 2012 |
| Series: | Graduate texts in mathematics
218 |
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Table of Contents:
- Preface
- 1 Smooth Manifolds
- 2 Smooth Maps
- 3 Tangent Vectors
- 4 Submersions, Immersions, and Embeddings
- 5 Submanifolds
- 6 Sard's Theorem
- 7 Lie Groups
- 8 Vector Fields
- 9 Integral Curves and Flows
- 10 Vector Bundles
- 11 The Cotangent Bundle
- 12 Tensors
- 13 Riemannian Metrics
- 14 Differential Forms
- 15 Orientations
- 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem
- 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22 Symplectic Manifolds
- Appendix A: Review of Topology
- Appendix B: Review of Linear Algebra
- Appendix C: Review of Calculus
- Appendix D: Review of Differential Equations
- References
- Notation Index
- Subject Index