Algebraic Topology Via Differential Geometry

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Cambridge University Press, 1987 - Mathematics - 363 pages
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In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.
 

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Contents

ALGEBRAIC PRELIMINARIES
1
DIFFERENTIAL FORMS ON AN OPEN SUBSET OF Rⁿ
30
DIFFERENTIABLE MANIFOLDS
70
DE RHAM COHOMOLOGY OF DIFFERENTIABLE MANIFOLDS
121
COMPUTING COHOMOLOGY
161
POINCARE DUALITY LEFSCHETZ THEOREM
214
STOKES THEOREM
319
CHERN CHARACTER AND NONCOMMUTATIVE DE RHAM HOMOLOGY
333
BIBLIOGRAPHY
360
INDEX
361
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