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From calculus to cohomology: De Rham cohomology and characteristic classes Ib H. Madsen, Jxrgen Tornehave
Publisher: CUP

À�PR】From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. Ã�グナロクオンライン 9thアニバーサリーパッケージ. The de Rham cohomology of a manifold is the subject of Chapter 6. [PR]ラグナロクオンライン 9thアニバーサリーパッケージ. On Chern-Weil theory: principal bundles with connections and their characteristic classes. Keywords: Manifolds with boundary, b-calculus, noncommutative geometry, Connes–Chern character, relative cyclic cohomology, -invariant. Topics include: Poincare lemma, calculation of de Rham cohomology for simple examples, the cup product and a comparison of homology with cohomology. Loop Spaces, Characteristic Classes and Geometric Quantization (Modern Birkhauser Classics) by Jean-luc Brylinski: This book deals with the differential geometry of. From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. Differentiable Manifolds DeRham Differential geometry and the calculus of variations hermann Geometry of Characteristic Classes Chern Geometry . Related 0 Algebraic and analytic preliminaries; 1 Basic concepts; II Vector bundles; III Tangent bundle and differential forms; IV Calculus of differential forms; V De Rham cohomology; VI Mapping degree; VII Integration over the fiber; VIII Cohomology of sphere bundles; IX Cohomology of vector bundles; X The Lefschetz class of a manifold; Appendix A The exponential map. MSC (2010): Primary 58Jxx, 46L80; Blowing-up the metric one recovers the pair of characteristic currents that represent the corresponding de Rham relative homology class, while the blow-down yields a relative cocycle whose expression involves higher eta cochains and their b-analogues.