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Homotopy Limits, Completions and Localizations

  • Aldridge K. Bousfield
  • Daniel M. Kan

Part of the Lecture Notes in Mathematics book series (LNM, volume 304)

Table of contents

  1. Front Matter
    Pages I-V
  2. Completions and localizations

    1. Front Matter
      Pages 1-9
    2. Aldridge K. Bousfield, Daniel M. Kan
      Pages 10-47
    3. Aldridge K. Bousfield, Daniel M. Kan
      Pages 48-69
    4. Aldridge K. Bousfield, Daniel M. Kan
      Pages 70-98
    5. Aldridge K. Bousfield, Daniel M. Kan
      Pages 99-125
    6. Aldridge K. Bousfield, Daniel M. Kan
      Pages 126-162
    7. Aldridge K. Bousfield, Daniel M. Kan
      Pages 163-201
    8. Aldridge K. Bousfield, Daniel M. Kan
      Pages 202-223
  3. Towers of fibrations, cosimplicial spaces and homotopy limits

    1. Front Matter
      Pages 224-227
    2. Aldridge K. Bousfield, Daniel M. Kan
      Pages 228-248
    3. Aldridge K. Bousfield, Daniel M. Kan
      Pages 249-264
    4. Aldridge K. Bousfield, Daniel M. Kan
      Pages 265-286
    5. Aldridge K. Bousfield, Daniel M. Kan
      Pages 287-324
    6. Aldridge K. Bousfield, Daniel M. Kan
      Pages 325-340
  4. Errata

    1. Aldridge K. Bousfield, Daniel M. Kan
      Pages 349-349
    2. Aldridge K. Bousfield, Daniel M. Kan
      Pages 349-349
    3. Aldridge K. Bousfield, Daniel M. Kan
      Pages 349-349
  5. Back Matter
    Pages 341-348

About this book

Introduction

The main purpose of part I of these notes is to develop for a ring R a functional notion of R-completion of a space X. For R=Zp and X subject to usual finiteness condition, the R-completion coincides up to homotopy, with the p-profinite completion of Quillen and Sullivan; for R a subring of the rationals, the R-completion coincides up to homotopy, with the localizations of Quillen, Sullivan and others. In part II of these notes, the authors have assembled some results on towers of fibrations, cosimplicial spaces and homotopy limits which were needed in the discussions of part I, but which are of some interest in themselves.

Keywords

Finite Homotopy fibrations function

Authors and affiliations

  • Aldridge K. Bousfield
    • 1
  • Daniel M. Kan
    • 2
  1. 1.Department of MathematicsUniversity of IllinoisChicagoUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-38117-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1972
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-06105-2
  • Online ISBN 978-3-540-38117-4
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site