Algebraic Topology via Differential Geometry

by M. Karoubi, C. Leruste

Overview

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.

Product Details

ISBN-13:	9780521317146
Publisher:	Cambridge University Press
Publication date:	01/07/1988
Series:	London Mathematical Society Lecture Note Series , #99
Edition description:	New Edition
Pages:	376
Product dimensions:	5.98(w) x 8.98(h) x 0.94(d)

Table of Contents

Introduction; 1. Algebraic preliminaries; 2. differential forms on an open subset of Rn; 3. differentiable manifolds; 4. De Rham cohomology of differentiable manifolds; 5. Computing cohomology; 6. Poincaré duality - Lefschetz' theorem; Appendixes; Bibliography; Index.