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Homotopy limits, completions and localizations

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 rati...

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Detalles Bibliográficos
Autores principales: Bousfield, Aldridge K, Kan, Daniel M
Lenguaje:eng
Publicado: Springer 1972
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-540-38117-4
http://cds.cern.ch/record/1690979
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author Bousfield, Aldridge K
Kan, Daniel M
author_facet Bousfield, Aldridge K
Kan, Daniel M
author_sort Bousfield, Aldridge K
collection CERN
description 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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institution Organización Europea para la Investigación Nuclear
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publishDate 1972
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spelling cern-16909792021-04-21T21:12:26Zdoi:10.1007/978-3-540-38117-4http://cds.cern.ch/record/1690979engBousfield, Aldridge KKan, Daniel MHomotopy limits, completions and localizationsMathematical Physics and MathematicsThe 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.Springeroai:cds.cern.ch:16909791972
spellingShingle Mathematical Physics and Mathematics
Bousfield, Aldridge K
Kan, Daniel M
Homotopy limits, completions and localizations
title Homotopy limits, completions and localizations
title_full Homotopy limits, completions and localizations
title_fullStr Homotopy limits, completions and localizations
title_full_unstemmed Homotopy limits, completions and localizations
title_short Homotopy limits, completions and localizations
title_sort homotopy limits, completions and localizations
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-540-38117-4
http://cds.cern.ch/record/1690979
work_keys_str_mv AT bousfieldaldridgek homotopylimitscompletionsandlocalizations
AT kandanielm homotopylimitscompletionsandlocalizations