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Boundedly Controlled Topology

Foundations of Algebraic Topology and Simple Homotopy Theory

  • Book
  • © 1988

Overview

Authors:
  1. Douglas R. Anderson
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  2. Hans J. Munkholm
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1323)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
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  2. Category theoretic foundations

    • Douglas R. Anderson, Hans J. Munkholm
    Pages 1-39

  3. The algebraic topology of boundedly controlled spaces

    • Douglas R. Anderson, Hans J. Munkholm
    Pages 40-98

  4. The geometric, boundedly controlled whitehead group

    • Douglas R. Anderson, Hans J. Munkholm
    Pages 99-122

  5. Free and projective rpg modules the algebraic whitehead groups of rpg

    • Douglas R. Anderson, Hans J. Munkholm
    Pages 123-175

  6. The isomorphism between the geometric and algebraic whitehead groups

    • Douglas R. Anderson, Hans J. Munkholm
    Pages 176-211

  7. Boundedly controlled manifolds and the s-cobordism theorem

    • Douglas R. Anderson, Hans J. Munkholm
    Pages 212-259

  8. Toward computations

    • Douglas R. Anderson, Hans J. Munkholm
    Pages 260-300

  9. Back Matter

    Pages 301-309
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Keywords

About this book

Several recent investigations have focused attention on spaces and manifolds which are non-compact but where the problems studied have some kind of "control near infinity". This monograph introduces the category of spaces that are "boundedly controlled" over the (usually non-compact) metric space Z. It sets out to develop the algebraic and geometric tools needed to formulate and to prove boundedly controlled analogues of many of the standard results of algebraic topology and simple homotopy theory. One of the themes of the book is to show that in many cases the proof of a standard result can be easily adapted to prove the boundedly controlled analogue and to provide the details, often omitted in other treatments, of this adaptation. For this reason, the book does not require of the reader an extensive background. In the last chapter it is shown that special cases of the boundedly controlled Whitehead group are strongly related to lower K-theoretic groups, and the boundedly controlled theory is compared to Siebenmann's proper simple homotopy theory when Z = IR or IR2.

Bibliographic Information

  • Book Title: Boundedly Controlled Topology

  • Book Subtitle: Foundations of Algebraic Topology and Simple Homotopy Theory

  • Authors: Douglas R. Anderson, Hans J. Munkholm

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0079806

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19397-5Published: 22 June 1988

  • eBook ISBN: 978-3-540-39249-1Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 310

  • Topics: Algebraic Topology

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