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

From calculus to cohomology: De Rham cohomology and characteristic classes Ib H. Madsen, Jxrgen Tornehave ebook
Publisher: CUP
ISBN: 0521589568, 9780521589567
Format: djvu
Page: 290

Topics include: Poincare lemma, calculation of de Rham cohomology for simple examples, the cup product and a comparison of homology with cohomology. Where “integration” means actual integration in the de Rham theory, or equivalently pairing with the fundamental homology class. Download Free eBook:From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes - Free chm, pdf ebooks rapidshare download, ebook torrents bittorrent download. Differentiable Manifolds DeRham Differential geometry and the calculus of variations hermann Geometry of Characteristic Classes Chern Geometry . On Chern-Weil theory: principal bundles with connections and their characteristic classes. From calculus to cohomology: de Rham cohomology and characteristic classes "Ib Henning Madsen, Jørgen Tornehave" 1997 Cambridge University Press 521589569. 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. Using “calculus” (or cohomology): let {[N], [N'] \in H^*(M be the fundamental classes. 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. Keywords: Manifolds with boundary, b-calculus, noncommutative geometry, Connes–Chern character, relative cyclic cohomology, -invariant. From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. Loop Spaces, Characteristic Classes and Geometric Quantization (Modern Birkhauser Classics) by Jean-luc Brylinski: This book deals with the differential geometry of. Then we have: \displaystyle | N \cap N'| = \int_M [N] \. The de Rham cohomology of a manifold is the subject of Chapter 6. Connections Curvature and Characteristic Classes From Calculus to Cohomology: De Rham Cohomology and Characteristic. Caveat: The “cardinality” of {N \cap N'} is really a signed one: each point is is not really satisfactory if we are working in characteristic {p} .