Contents
Preface
CHAPTER I. Manifolds and Vector Fields
1. Differentiate Manifolds
2. Submersions and Immersions
3. Vector Fields and Flows
CHAPTER II. Lie Groups and Group Actions
4. Lie Groups I
5. Lie Groups II. Lie Subgroups and Homogeneous Spaces
6. Transformation Groups and G-Manifolds
7. Polynomial and Smooth Invariant Theory
CHAPTER III. Differential Forms and de Rham Cohomology
8. Vector Bundles
9. Differential Forms
10. Integration on Manifolds
11. De Rham Cohomology
12. Cohomology with Compact Supports and Poincare Duality
13. De Rham Cohomology of Compact Manifolds
14. Lie Groups III. Analysis on Lie Groups
15. Extensions of Lie Algebras and Lie Groups
