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Homotopy Limits, Completions and Localizations

  • Book
  • © 1972

Overview

Authors:
  1. Aldridge K. Bousfield

    1. Department of Mathematics, University of Illinois, Chicago, USA

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  2. Daniel M. Kan

    1. Massachusetts Institute of Technology, Cambridge, USA

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-V
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  2. Completions and localizations

    1. Front Matter

      Pages 1-9
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    2. The R-completion of a space

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 10-47

    3. Fibre lemmas

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 48-69

    4. Tower lemmas

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 70-98

    5. An R-completion of groups and its relation to the R-completion of spaces

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 99-125

    6. R-localizations of nilpotent spaces

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 126-162

    7. p-completions of nilpotent spaces

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 163-201

    8. A glimpse at the R-completion of non-nilpotent spaces

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 202-223

  3. Towers of fibrations, cosimplicial spaces and homotopy limits

    1. Front Matter

      Pages 224-227
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    2. Simplicial sets and topological spaces

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 228-248

    3. Towers of fibrations

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 249-264

    4. Cosimplicial spaces

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 265-286

    5. Homotopy inverse limits

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 287-324

    6. Homotopy direct limits

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 325-340

  4. Errata

    1. Erratum to: Tower lemmas

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 349-349

    2. Erratum to: The R-completion of a space

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 349-349

    3. Erratum to: p-completions of nilpotent spaces

      • Aldridge K. Bousfield, Daniel M. Kan
      Pages 349-349

  5. Back Matter

    Pages 341-348
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Illinois, Chicago, USA

    Aldridge K. Bousfield

  • Massachusetts Institute of Technology, Cambridge, USA

    Daniel M. Kan

Bibliographic Information

  • Book Title: Homotopy Limits, Completions and Localizations

  • Authors: Aldridge K. Bousfield, Daniel M. Kan

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-38117-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1972

  • Softcover ISBN: 978-3-540-06105-2Published: 20 December 1972

  • eBook ISBN: 978-3-540-38117-4Published: 20 March 2009

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 352

  • Topics: Topology, Algebraic Topology

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