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

Cambridge University Press | 1997 | ISBN: 0521589568 | 296 pages | PDF | 12 MB. Then we have: \displaystyle | N \cap N'| = \int_M [N] \. 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} . From calculus to cohomology: de Rham cohomology and characteristic classes "Ib Henning Madsen, Jørgen Tornehave" 1997 Cambridge University Press 521589569. Differentiable Manifolds DeRham Differential geometry and the calculus of variations hermann Geometry of Characteristic Classes Chern Geometry . Using “calculus” (or cohomology): let {[N], [N'] \in H^*(M be the fundamental classes. Free Direct Download From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. Topics include: Poincare lemma, calculation of de Rham cohomology for simple examples, the cup product and a comparison of homology with cohomology. The de Rham cohomology of a manifold is the subject of Chapter 6. Where “integration” means actual integration in the de Rham theory, or equivalently pairing with the fundamental homology class. 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. Connections Curvature and Characteristic Classes From Calculus to Cohomology: De Rham Cohomology and Characteristic.