Algebraic Topology via Differential Geometry

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Paperback | 7 March 1988

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376 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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Non-Fiction Mathematics Topology Geometry Differential & Riemannian Geometry Algebra Probability & Statistics

Introduction	p. ix
Algebraic preliminaries	p. 1
Differential forms on an open subset of R[superscript n]	p. 30
Differentiable manifolds	p. 70
De Rham cohomology of differentiable manifolds	p. 121
Computing cohomology	p. 161
Poincare duality-Lefschetz' theorem	p. 214
Stokes' theorem	p. 319
Chem character and non-commutative De Rham cohomology	p. 333
Bibliography	p. 360
Index	p. 361
Table of Contents provided by Syndetics. All Rights Reserved.

Algebraic Topology via Differential Geometry

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