Preface |
Introduction / Chapter 1: |
The Alternating Algebra / Chapter 2: |
de Rham Cohomology / Chapter 3: |
Chain Complexes and their Cohomology / Chapter 4: |
The Mayer-Vietoris Sequence / Chapter 5: |
Homotopy / Chapter 6: |
Applications of de Rham Cohomology / Chapter 7: |
Smooth Manifolds / Chapter 8: |
Differential Forms on Smoth Manifolds / Chapter 9: |
Integration on Manifolds / Chapter 10: |
Degree, Linking Numbers and Index of Vector Fields / Chapter 11: |
The Poincare-Hopf Theorem / Chapter 12: |
Poincare Duality / Chapter 13: |
The Complex Projective Space CP[superscript n] / Chapter 14: |
Fiber Bundles and Vector Bundles / Chapter 15: |
Operations on Vector Bundles and their Sections / Chapter 16: |
Connections and Curvature / Chapter 17: |
Characteristic Classes of Complex Vector Bundles / Chapter 18: |
The Euler Class / Chapter 19: |
Cohomology of Projective and Grassmannian Bundles / Chapter 20: |
Thom Isomorphism and the General Gauss-Bonnet Formula / Chapter 21: |
Smooth Partition of Unity / Appendix A: |
Invariant Polynomials / Appendix B: |
Proof of Lemmas 12.12 and 12.13 / Appendix C: |
Exercises / Appendix D: |
References |
Index |
The alternating algebra / 1: |
De Rham cohomology / 3: |
Chain complexes and their cohomology / 4: |
The Mayer-Vietoris sequence / 5: |
Applications of De Rham cohomology / 6: |
Smooth manifolds / 8: |
Differential forms on smooth manifolds / 9: |
Integration on manifolds / 10: |
Degree, linking numbers and index of vector fields / 11: |
The Poincare-Hopf theorem / 12: |
Poincare duality / 13: |
The complex projective space CPn / 14: |
Fiber bundles and vector bundles / 15: |
Operations on vector bundles and their sections / 16: |
Connections and curvature / 17: |
Characteristic classes of complex vector bundles / 18: |
The Euler class / 19: |
Cohomology of projective and Grassmanian bundles / 20: |
Thom isomorphism and the general Gauss-Bonnet formula / 21: |
Preface |
Introduction / Chapter 1: |
The Alternating Algebra / Chapter 2: |
de Rham Cohomology / Chapter 3: |
Chain Complexes and their Cohomology / Chapter 4: |
The Mayer-Vietoris Sequence / Chapter 5: |