Homotopy Limits, Completions and Localizations / Edition 1

Homotopy Limits, Completions and Localizations / Edition 1

by A. K. Bousfield, D. M. Kan
     
 

ISBN-10: 3540061053

ISBN-13: 9783540061052

Pub. Date: 05/01/1987

Publisher: Springer Berlin Heidelberg

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

Overview

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.

Product Details

ISBN-13:
9783540061052
Publisher:
Springer Berlin Heidelberg
Publication date:
05/01/1987
Series:
Lecture Notes in Mathematics Series, #304
Edition description:
1st ed. 1972. 2nd printing 1987
Pages:
352
Product dimensions:
6.69(w) x 9.61(h) x 0.74(d)

Related Subjects

Table of Contents

Completions and localizations.- The R-completion of a space.- Fibre lemmas.- Tower lemmas.- An R-completion of groups and its relation to the R-completion of spaces.- R-localizations of nilpotent spaces.- p-completions of nilpotent spaces.- A glimpse at the R-completion of non-nilpotent spaces.- Towers of fibrations, cosimplicial spaces and homotopy limits.- Simplicial sets and topological spaces.- Towers of fibrations.- Cosimplicial spaces.- Homotopy inverse limits.- Homotopy direct limits.- Errata.- Erratum to: The R-completion of a space.- Erratum to: Tower lemmas.- Erratum to: p-completions of nilpotent spaces.

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