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

Madsen, Jxrgen Tornehave, "From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes" Cambridge University Press | 1997 | ISBN: 0521589568 | 296 pages | PDF | 12 MB. On Chern-Weil theory: principal bundles with connections and their characteristic classes. From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. Where “integration” means actual integration in the de Rham theory, or equivalently pairing with the fundamental homology class. 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. 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} . It is a useful reference, in particular for those advanced undergraduates and graduate From Calculus to Cohomology: De Rham Cohomology and Characteristic. De Rham cohomology is the cohomology of differential forms. Euler class - Wikipedia, the free encyclopedia in the cohomology of E relative to the complement E\E 0 of the zero section E 0.. Using “calculus” (or cohomology): let {[N], [N'] \in H^*(M be the fundamental classes. Download Download Cohomology of Vector Bundles & Syzgies .