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Homotopy pull-back squares up to localization
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH.
KTH.
2006 (English)In: Alpine Anthology of Homotopy Theory / [ed] Arlettaz, D; Hess, K, PROVIDENCE: AMER MATHEMATICAL SOC , 2006, Vol. 399, 55-72 p.Conference paper, Published paper (Refereed)
Abstract [en]

We characterize the class of homotopy pull-back squares by means of elementary closure properties. The so called Puppe theorem which identifies the homotopy fiber of certain maps constructed as homotopy colimits is a straightforward consequence. Likewise we characterize the class of squares which are homotopy pull-backs "up to Bousfield localization". This yields a generalization of Puppe's theorem which allows us to identify the homotopy type of the localized homotopy fiber. When the localization functor is homological localization this is one of the key ingredients in the group completion theorem.

Place, publisher, year, edition, pages
PROVIDENCE: AMER MATHEMATICAL SOC , 2006. Vol. 399, 55-72 p.
Series
CONTEMPORARY MATHEMATICS SERIES, ISSN 0271-4132 ; 399
Keyword [en]
group completion, Bousfield localization, homotopy pull-back, homotopy colimit, fiberwise construction, model category
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-42108ISI: 000237280300004ISBN: 0-8218-3696-X (print)OAI: oai:DiVA.org:kth-42108DiVA: diva2:446094
Conference
2nd Arolla Conference on Algebraic Topology. Arolla, SWITZERLAND. AUG 24-29, 2004
Note
QC 20111006Available from: 2011-10-06 Created: 2011-10-05 Last updated: 2011-10-06Bibliographically approved

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  • apa
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  • en-US
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  • nn-NB
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  • Other locale
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Output format
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