Connections, Curvature, and Cohomology V1: De Rham cohomology of manifolds and vector bundlesConnections, Curvature, and Cohomology V1 |
Contents
| 1 | |
| 15 | |
Chapter II Vector Bundles | 44 |
Chapter III Tangent Bundle and Differential Forms | 87 |
Chapter IV Calculus of Differential Forms | 141 |
Chapter V De Rham Cohomology | 176 |
Chapter VI Mapping Degree | 240 |
Chapter VII Integration over the Fibre | 280 |
Chapter X The Lefschetz Class of a Manifold | 391 |
Appendix A The Exponential Map | 418 |
References | 423 |
Bibliography | 425 |
| 431 | |
| 433 | |
| 435 | |
| 444 | |
Common terms and phrases
a₁ Assume B₁ bundle map called carr Choose cohomology connected consider coordinate representation cross-section defined definition dega denote determinant function diffeomorphism differential forms e₁ Euclidean space Euler class Example fibre preserving follows given graded algebras Hence homogeneous of degree homomorphism homotopic HP(M inclusion map induces integral isolated zero Lemma Let f Let q linear isomorphism linear map map q module neighbourhood obtain open cover open sets open subset orientation preserving oriented n-manifold p-form Proof Proposition VIII Q.E.D. Corollary represents resp restriction Riemannian metric satisfies Show smooth bundle smooth function smooth map sphere bundle strong bundle map subbundle submanifold Suppose surjective tangent bundle Theorem topology trivial U₁ U₂ unit sphere V₁ vector bundle vector field vector space αε βε Φα χε