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



From calculus to cohomology: De Rham cohomology and characteristic classes ebook




From calculus to cohomology: De Rham cohomology and characteristic classes Ib H. Madsen, Jxrgen Tornehave ebook
Format: djvu
Publisher: CUP
ISBN: 0521589568, 9780521589567
Page: 290


Madsen, Jxrgen Tornehave, "From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes" Cambridge University Press | 1997 | ISBN: 0521589568 | 296 pages | PDF | 12 MB. Keywords: Manifolds with boundary, b-calculus, noncommutative geometry, Connes–Chern character, relative cyclic cohomology, -invariant. Topics include: Poincare lemma, calculation of de Rham cohomology for simple examples, the cup product and a comparison of homology with cohomology. 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. Differentiable Manifolds DeRham Differential geometry and the calculus of variations hermann Geometry of Characteristic Classes Chern Geometry . 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. Loop Spaces, Characteristic Classes and Geometric Quantization (Modern Birkhauser Classics) by Jean-luc Brylinski: This book deals with the differential geometry of. For a representative of the characteristic class called the first fractional Pontryagin class. Represents the image in de Rham cohomology of a generators of the integral cohomology group H 3 ( G , ℤ ) ≃ ℤ . On Chern-Weil theory: principal bundles with connections and their characteristic classes. De Rham cohomology is the cohomology of differential forms. From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes. The de Rham cohomology of a manifold is the subject of Chapter 6.