From Calculus to Cohomology: de Rham cohomology and characteristic classes

Cover
Title page
Preface
Chapter 1 Introduction
Chapter 2 The Altemating Algebra
Chapter 3 de Rham Cohomology
Chapter 4 Chain Complexes and their Cohomology
Chapter 5 The Mayer-Vietoris Sequence
Chapter 6 Homotopy
Chapter 7 Applications of de Rham Cohomology
Chapter 8 Smooth Manifolds
Chapter 9 Differential Forms on Smooth Manifolds
Chapter 10 Integration on Manifolds
Chapter 11 Degree, Linking Numbers and Index of Vector Fields
Chapter 12 The Poincaré-Hopf Theorem
Chapter 13 Poincaré Duality
Chapter 14 The Complex Projective Space CP^n
Chapter 15 Fiber Bundles and Vector Bundles
Chapter 16 Operations on Vector Bundles and their Sections
Chapter 17 Connections and Curvature
Chapter 18 Characteristic Classes of Complex Vector Bundles
Chapter 19 The Euler Class
Chapter 20 Cohomology of Projective and Grassmannian Bundles
Chapter 21 Thom Isomorphism and the General Gauss-Bonnet Formula
Appendix A Smooth Partition of Unity
Appendix B Invariant Polynomials
Appendix C Proof of Lemmas 12.12 and 12.13
Appendix D Exercises
References
Index