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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
ISBN: 0521589568, 9780521589567
Publisher: CUP
Page: 290
Format: djvu

Cambridge University Press | 1997 | ISBN: 0521589568 | 296 pages | PDF | 12 MB. For a representative of the characteristic class called the first fractional Pontryagin class. Keywords: Manifolds with boundary, b-calculus, noncommutative geometry, Connes–Chern character, relative cyclic cohomology, -invariant. Then we have: \displaystyle | N \cap N'| = \int_M [N] \. From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. The de Rham cohomology of a manifold is the subject of Chapter 6. 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} . Free Direct Download From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. Connections Curvature and Characteristic Classes From Calculus to Cohomology: De Rham Cohomology and Characteristic. Using “calculus” (or cohomology): let {[N], [N'] \in H^*(M be the fundamental classes. Topics include: Poincare lemma, calculation of de Rham cohomology for simple examples, the cup product and a comparison of homology with cohomology. Represents the image in de Rham cohomology of a generators of the integral cohomology group H 3 ( G , ℤ ) ≃ ℤ . 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. Where “integration” means actual integration in the de Rham theory, or equivalently pairing with the fundamental homology class.