Introduction to Smooth Manifolds

• Main Author: Lee, John M. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2012.
• Edition: 2nd ed. 2012.
• Series: Graduate Texts in Mathematics, 218
• Subjects: Mathematics.; Differential geometry.; Differential Geometry.

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...

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.