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

Using “calculus” (or cohomology): let {[N], [N'] \in H^*(M be the fundamental classes. Represents the image in de Rham cohomology of a generators of the integral cohomology group H 3 ( G , ℤ ) ≃ ℤ . Keywords: Manifolds with boundary, b-calculus, noncommutative geometry, Connes–Chern character, relative cyclic cohomology, -invariant. The results on differentiable Lie group cohomology used above are in. From calculus to cohomology: de Rham cohomology and characteristic classes "Ib Henning Madsen, Jørgen Tornehave" 1997 Cambridge University Press 521589569. From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. For a representative of the characteristic class called the first fractional Pontryagin 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. Blanc, Cohomologie différentiable et changement de groupes Astérisque, vol. Where “integration” means actual integration in the de Rham theory, or equivalently pairing with the fundamental homology class. 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} . Then we have: \displaystyle | N \cap N'| = \int_M [N] \.