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Cambridge University Press

From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes

From Calculus to Cohomology: de Rham Cohomology and Characteristic Classes

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De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last eleven chapters cover Morse theory, index of vector fields, Poincar duality, vector bundles, connections and curvature, Chern and Euler classes, Thom isomorphism, and the general Gauss-Bonnet theorem. The text includes over 150 exercises, and gives the background necessary for the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology. It will be invaluable to anyone who wishes to know about cohomology, curvature, and their applications.

Author: Ib Madsen, Madsen/Tornehave
Publisher: Cambridge University Press
Published: 03/13/1997
Pages: 296
Binding Type: Paperback
Weight: 1.13lbs
Size: 9.36h x 7.54w x 0.64d
ISBN: 9780521589567

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