A User’s Guide to Algebraic Topology: 387 (Mathematics and Its Applications, 387) - Hardcover

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

Hardcover

ISBN 10: 0792342925 ISBN 13: 9780792342922

Publisher: Springer, 1996

Synopsis

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.

About this title

Synopsis

This volume arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature rather than in developing the theory. Typical areas of applications are differential geometry and theoretical physics. The text starts with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. After this, it is shown how to calculate homotopy groups, homology groups and cohomology rings of most of the major theories, exact homotopy sequences of fibrations, some important spectral sequences, and all the obstructions that can be computed from these. The approach used is to mix illustrative examples with those proofs that actually develop transferable calculational aids. Extensive appendices with notes on background material are given, along with tables.

Edition details

• Publisher: Springer
• Publication date: 1996
• Language: English
• ISBN 10: 0792342925
• ISBN 13: 9780792342922
• Binding: Hardcover
• Number of pages: 422