Localizing with respect to self-maps of the circle

We describe a general procedure to construct idempotent functors on the pointed homotopy category of connected $ {\text{CW}}$-complexes, some of which extend $ P$-localization of nilpotent spaces, at a set of primes $ P$. We focus our attention on one such functor, whose local objects are $ {\text{C...

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Detalhes bibliográficos
Autores: Casacuberta, Carles, Peschke, Georg
Formato: artículo
Estado:Versión publicada
Fecha de publicación:1993
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/96481
Acesso em linha:https://hdl.handle.net/2445/96481
Access Level:acceso abierto
Palavra-chave:Teoria de l'homotopia
Àlgebra homològica
Teoria de grups
Topologia algebraica
Homotopy theory
Homological algebra
Group theory
Algebraic topology
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spelling Localizing with respect to self-maps of the circleCasacuberta, CarlesPeschke, GeorgTeoria de l'homotopiaÀlgebra homològicaTeoria de grupsTopologia algebraicaHomotopy theoryHomological algebraGroup theoryAlgebraic topologyWe describe a general procedure to construct idempotent functors on the pointed homotopy category of connected $ {\text{CW}}$-complexes, some of which extend $ P$-localization of nilpotent spaces, at a set of primes $ P$. We focus our attention on one such functor, whose local objects are $ {\text{CW}}$-complexes $ X$ for which the $ p$th power map on the loop space $ \Omega X$ is a self-homotopy equivalence if $ p \notin P$. We study its algebraic properties, its behaviour on certain spaces, and its relation with other functors such as Bousfield's homology localization, Bousfield-Kan completion, and Quillen's plus-construction.American Mathematical Society (AMS)2016201619932016info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion24 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/96481Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-1993-1123451-XTransactions of the American Mathematical Society, 1993, vol. 339, num. 1, p. 117-140http://dx.doi.org/10.1090/S0002-9947-1993-1123451-X(c) American Mathematical Society (AMS), 1993info:eu-repo/semantics/openAccessoai:recercat.cat:2445/964812026-05-29T05:05:01Z
dc.title.none.fl_str_mv Localizing with respect to self-maps of the circle
title Localizing with respect to self-maps of the circle
spellingShingle Localizing with respect to self-maps of the circle
Casacuberta, Carles
Teoria de l'homotopia
Àlgebra homològica
Teoria de grups
Topologia algebraica
Homotopy theory
Homological algebra
Group theory
Algebraic topology
title_short Localizing with respect to self-maps of the circle
title_full Localizing with respect to self-maps of the circle
title_fullStr Localizing with respect to self-maps of the circle
title_full_unstemmed Localizing with respect to self-maps of the circle
title_sort Localizing with respect to self-maps of the circle
dc.creator.none.fl_str_mv Casacuberta, Carles
Peschke, Georg
author Casacuberta, Carles
author_facet Casacuberta, Carles
Peschke, Georg
author_role author
author2 Peschke, Georg
author2_role author
dc.subject.none.fl_str_mv Teoria de l'homotopia
Àlgebra homològica
Teoria de grups
Topologia algebraica
Homotopy theory
Homological algebra
Group theory
Algebraic topology
topic Teoria de l'homotopia
Àlgebra homològica
Teoria de grups
Topologia algebraica
Homotopy theory
Homological algebra
Group theory
Algebraic topology
description We describe a general procedure to construct idempotent functors on the pointed homotopy category of connected $ {\text{CW}}$-complexes, some of which extend $ P$-localization of nilpotent spaces, at a set of primes $ P$. We focus our attention on one such functor, whose local objects are $ {\text{CW}}$-complexes $ X$ for which the $ p$th power map on the loop space $ \Omega X$ is a self-homotopy equivalence if $ p \notin P$. We study its algebraic properties, its behaviour on certain spaces, and its relation with other functors such as Bousfield's homology localization, Bousfield-Kan completion, and Quillen's plus-construction.
publishDate 1993
dc.date.none.fl_str_mv 1993
2016
2016
2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/96481
url https://hdl.handle.net/2445/96481
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-1993-1123451-X
Transactions of the American Mathematical Society, 1993, vol. 339, num. 1, p. 117-140
http://dx.doi.org/10.1090/S0002-9947-1993-1123451-X
dc.rights.none.fl_str_mv (c) American Mathematical Society (AMS), 1993
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Mathematical Society (AMS), 1993
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 24 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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