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
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