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Cover: 9783540061052 | Homotopy Limits, Completions and Localizations | D. M. Kan (u. a.)
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Homotopy Limits, Completions and Localizations
Taschenbuch von D. M. Kan (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
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.
Details
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 356
Reihe: Lecture Notes in Mathematics
ISBN-13: 9783540061052
ISBN-10: 3540061053
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kan, D. M.
Bousfield, A. K.
Auflage: 1972
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Mathematics
Maße: 242 x 170 x 20 mm
Von/Mit: D. M. Kan (u. a.)
Erscheinungsdatum: 01.05.1987
Gewicht: 0,61 kg
preigu-id: 102160960
Inhaltsverzeichnis
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.
Details
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 356
Reihe: Lecture Notes in Mathematics
ISBN-13: 9783540061052
ISBN-10: 3540061053
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kan, D. M.
Bousfield, A. K.
Auflage: 1972
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Lecture Notes in Mathematics
Maße: 242 x 170 x 20 mm
Von/Mit: D. M. Kan (u. a.)
Erscheinungsdatum: 01.05.1987
Gewicht: 0,61 kg
preigu-id: 102160960
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