Homotopy Limits, Completions and Localizations. 1st ed. 1972

種類:

電子ブック

責任表示:

by A. K. Bousfield, D. M. Kan

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1972

著者名:

• Bousfield, A. K.
• Kan, D. M.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 304

ISBN:

9783540381174 [3540381171]    

注記:

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.
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.

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