Introduction to Smooth Manifolds

by John M. Lee

The preface and Chapter 1 are available for downloading in PDF format.  You need the Adobe Acrobat Reader to view them.

Preface

  1. Smooth Manifolds
  2. Smooth Maps
  3. Tangent Vectors
  4. Vector Fields
  5. Vector Bundles
  6. The Cotangent Bundle
  7. Submersions, Immersions, and Embeddings
  8. Submanifolds
  9. Lie Group Actions
  10. Embedding and Approximation Theorems
  11. Tensors
  12. Differential Forms
  13. Orientations
  14. Integration on Manifolds
  15. De Rham Cohomology
  16. The de Rham Theorem
  17. Integral Curves and Flows
  18. Lie Derivatives
  19. Integral Manifolds and Foliations
  20. Lie Groups and Their Lie Algebras
Appendix: Review of Prerequisites

References

Index

Introduction to Smooth Manifolds