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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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Lenguaje: | eng |
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Springer
1972
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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. |
id | cern-1690979 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 1972 |
publisher | Springer |
record_format | invenio |
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 |