A User's Guide to Algebraic Topology / Edition 1

by C.T. Dodson, P.E. Parker

Overview

We have tried to design this book for both instructional and reference use, during and after a first course in algebraic topology aimed at users rather than developers; indeed, the book arose from such courses taught by the authors. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. A certain amount of redundancy is built in for the reader's convenience: we hope to minimize :fiipping back and forth, and we have provided some appendices for reference. The first three are concerned with background material in algebra, general topology, manifolds, geometry and bundles. Another gives tables of homo­ topy groups that should prove useful in computations, and the last outlines the use of a computer algebra package for exterior calculus. Our approach has been that whenever a construction from a proof is needed, we have explicitly noted and referenced this. In general, wehavenot given a proof unless it yields something useful for computations. As always, the only way to un­ derstand mathematics is to do it and use it. To encourage this, Ex denotes either an example or an exercise. The choice is usually up to you the reader, depending on the amount of work you wish to do; however, some are explicitly stated as ( unanswered) questions. In such cases, our implicit claim is that you will greatly benefit from at least thinking about how to answer them.

Product Details

ISBN-13:	9780792342922
Publisher:	Springer US
Publication date:	12/31/1996
Series:	Mathematics and Its Applications , #387
Edition description:	1997
Pages:	410
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Preface. Introduction and Overview. 1. Basics of Extension and Lifting Problems. 2. Up to Homotopy is Good Enough. 3. Homotopy Group Theory. 4. Homology and Cohomology Theories. 5. Examples in Homology and Cohomology. 6. Sheaf and Spectral Theories. 7. Bundle Theory. 8. Obstruction Theory. 9. Applications. A: Algebra. B: Topology. C: Manifolds and Bundles. D: Tables of Homotopy Groups. E: Computational Algebraic Topology. Bibliography. Index.

Editorial Reviews

Designed for instructional and reference use, this primer in algebraic topology begins by illustrating the fundamental ideas and constructions in homotopy theory. It shows how to calculate homotopy groups, homology groups, and cohomology rings in most major theories, exact homotopy sequences of fibrations, important spectral sequences, and all the obstructions which can be computed from these. Annotation c. by Book News, Inc., Portland, Or.

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