A user's guide to algebraic topology

Bibliographic Information

A user's guide to algebraic topology

by C.T.J. Dodson and Phillip E. Parker

(Mathematics and its applications, v. 387)

Kluwer Academic Publishers, c1997

  • : Hb
  • : pbk

Available at  / 52 libraries

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Note

Includes bibliographical references (p. 385-392) and index

Description and Table of Contents

Description

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.

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.

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Details

  • NCID
    BA29446275
  • ISBN
    • 0792342925
    • 0792342933
  • LCCN
    96043438
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    xii, 405 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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