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
AP(M Assume basis bundle map called carr q Choose cohomology commutative diagram connected consider coordinate representation cross-section defined definition determinant function diffeomorphism differential forms Euclidean space Euler class Example fibre preserving follows given graded algebras graded differential algebras Hence homogeneous of degree homomorphism homotopic HP(M inclusion map induces integral isolated zero Lefschetz Lemma Let f Let q linear isomorphism linear map module neighbourhood obtain open cover open sets open subset orientation preserving oriented n-manifold p-form p-linear particular Poincaré pšp Proof Proposition VIII prove Q.E.D. Corollary represents resp Riemannian metric satisfies Show smooth bundle smooth function smooth manifold smooth map smooth map šp sphere bundle strong bundle map subbundle submanifold Suppose surjective tangent bundle tensor Theorem topology trivial unit sphere vector bundle vector field vector space