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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 10 chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The last 11 chapters cover Morse theory, index of vector fields, Poincare duality, vector bundles, connections and curvature, Chern and Euler classes, and Thom isomorphism, and the book ends with the general Gauss-Bonnet theorem.
The text includes well 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 anyone who wishes to know about cohomology, curvature, and their applications.
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From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes
1999, Cambridge University Press
Paperback
in English
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0521589568 9780521589567
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From calculus to cohomology: de Rham cohomology and characteristic classes
1997, Cambridge University Press
in English
0521589568 9780521589567
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Includes bibliographical references (p. 281) and index.
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- Created April 1, 2008
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August 5, 2023 | Edited by AgentSapphire | remove incorrect isbn |
August 5, 2023 | Edited by AgentSapphire | reverted to revision 17 |
August 5, 2023 | Edited by AgentSapphire | reverted to revision 6 |
November 23, 2020 | Edited by MARC Bot | import existing book |
April 1, 2008 | Created by an anonymous user | Imported from Scriblio MARC record |