Boundedly Controlled Topology

Foundations of Algebraic Topology and Simple Homotopy Theory

  • Authors
  • Douglas R. Anderson
  • Hans J. Munkholm
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1323)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Douglas R. Anderson, Hans J. Munkholm
    Pages 1-39
  3. Douglas R. Anderson, Hans J. Munkholm
    Pages 40-98
  4. Douglas R. Anderson, Hans J. Munkholm
    Pages 99-122
  5. Douglas R. Anderson, Hans J. Munkholm
    Pages 123-175
  6. Douglas R. Anderson, Hans J. Munkholm
    Pages 176-211
  7. Douglas R. Anderson, Hans J. Munkholm
    Pages 212-259
  8. Douglas R. Anderson, Hans J. Munkholm
    Pages 260-300
  9. Back Matter
    Pages 301-309

About this book

Introduction

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.

Keywords

Algebraic topology Homotopy homotopy theory topology

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0079806
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19397-5
  • Online ISBN 978-3-540-39249-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book