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Ib H. Madsen, Jxrgen Tornehave, "From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes"

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, Poincaré 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.

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	Study The Heart of Cohomology Goro Kato, The Heart of Cohomology Springer \| ISBN: 1402050356 \| 1 edition (November 14, 2006) \| 195 pages \| PDF \| 2.3 Mb If you have not heard about cohomology, this book may be suited for you. Fundamental notions in cohomology for exampl ...
	Science/Engineering Elliptic Cohomology Elliptic Cohomology (University Series in Mathematics): Charles B. Thomas Springer \| ISBN: 0306460971 \| October 1999 \| djvu (ocr) \| 349 pages \| 2.14 MB Elliptic cohomology is an extremely beautiful theory with both geometric and arithmeti ...
	Science/Engineering Generalized Cohomology Akira Kono, Dai Tamaki, "Generalized Cohomology" American Mathematical Society \| 2006 \| ISBN: 0821835149 \| 256 pages \| Djvu \| 2,8 MB In the 1950s, Eilenberg and Steenrod presented their famous characterization of homology theory by seve ...
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	Mathematics From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes Author: Ib Henning Madsen, Jørgen TornehavePublisher: Cambridge University PressPages: 286De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of charact ...

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