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

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. Keywords: Manifolds with boundary, b-calculus, noncommutative geometry, Connes–Chern character, relative cyclic cohomology, -invariant. Ãグナロクオンライン 9thアニバーサリーパッケージ. 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} . ÀPR】From Calculus to Cohomology: De Rham Cohomology and Characteristic 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. Topics include: Poincare lemma, calculation of de Rham cohomology for simple examples, the cup product and a comparison of homology with cohomology. Using “calculus” (or cohomology): let {[N], [N'] in H^*(M be the fundamental classes. Madsen, Jxrgen Tornehave, "From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes" Cambridge University Press | 1997 | ISBN: 0521589568 | 296 pages | PDF | 12 MB. Then we have: displaystyle | N cap N'| = int_M [N] . [PR]ラグナロクオンライン 9thアニバーサリーパッケージ.