Closed model categories for [n,m]-types

For m >= n > 0, a map f between pointed spaces is said to be a weak [n,m]-equivalence if f induces isomorphisms of the homotopy groups \pi_k for n <= k <= m∼. Associated with this notion we give two different closed model category structures to the category of pointed spaces. Both struct...

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Detalles Bibliográficos
Autores: Ignacio Extremiana Aldana, J., Hernandez Paricio, L.J. [0000-0003-4528-7781], Rivas Rodriguez, M.T. [0000-0001-8911-4941]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:1997
País:España
Institución:Universidad de La Rioja (UR)
Repositorio:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc6a15b750603269e826b7
Acceso en línea:https://investigacion.unirioja.es/documentos/5bbc6a15b750603269e826b7
Access Level:acceso abierto
Palabra clave:[n
m]-types
Closed model category
Homotopy category
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spelling Closed model categories for [n,m]-typesIgnacio Extremiana Aldana, J.Hernandez Paricio, L.J. [0000-0003-4528-7781]Rivas Rodriguez, M.T. [0000-0001-8911-4941][nm]-typesClosed model categoryHomotopy categoryFor m >= n > 0, a map f between pointed spaces is said to be a weak [n,m]-equivalence if f induces isomorphisms of the homotopy groups \pi_k for n <= k <= m∼. Associated with this notion we give two different closed model category structures to the category of pointed spaces. Both structures have the same class of weak equivalences but different classes of fibrations and therefore of cofibrations. Using one of these structures, one obtains that the localized category is equivalent to the category of n-reduced CW-complexes with dimension less than or equal to m+1 and m-homotopy classes of cellular pointed maps. Using the other structure we see that the localized category is also equivalent to the homotopy category of (n-1)-connected (m+1)-coconnected CW-complexes.1997info:eu-repo/semantics/articleSubtype: Articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://investigacion.unirioja.es/documentos/5bbc6a15b750603269e826b7reponame:RIUR. Repositorio Institucional de la Universidad de La Riojainstname:Universidad de La Rioja (UR)Inglésinfo:eu-repo/semantics/altIdentifier/pissn/1201-561XClosed model categories for [n,m]-types, 1997, vol. 3, núm. 10, pág. 251-266info:eu-repo/semantics/openAccessoai:portal.dialnet.es:doc/5bbc6a15b750603269e826b72026-06-14T12:47:17Z
dc.title.none.fl_str_mv Closed model categories for [n,m]-types
title Closed model categories for [n,m]-types
spellingShingle Closed model categories for [n,m]-types
Ignacio Extremiana Aldana, J.
[n
m]-types
Closed model category
Homotopy category
title_short Closed model categories for [n,m]-types
title_full Closed model categories for [n,m]-types
title_fullStr Closed model categories for [n,m]-types
title_full_unstemmed Closed model categories for [n,m]-types
title_sort Closed model categories for [n,m]-types
dc.creator.none.fl_str_mv Ignacio Extremiana Aldana, J.
Hernandez Paricio, L.J. [0000-0003-4528-7781]
Rivas Rodriguez, M.T. [0000-0001-8911-4941]
author Ignacio Extremiana Aldana, J.
author_facet Ignacio Extremiana Aldana, J.
Hernandez Paricio, L.J. [0000-0003-4528-7781]
Rivas Rodriguez, M.T. [0000-0001-8911-4941]
author_role author
author2 Hernandez Paricio, L.J. [0000-0003-4528-7781]
Rivas Rodriguez, M.T. [0000-0001-8911-4941]
author2_role author
author
dc.subject.none.fl_str_mv [n
m]-types
Closed model category
Homotopy category
topic [n
m]-types
Closed model category
Homotopy category
description For m >= n > 0, a map f between pointed spaces is said to be a weak [n,m]-equivalence if f induces isomorphisms of the homotopy groups \pi_k for n <= k <= m∼. Associated with this notion we give two different closed model category structures to the category of pointed spaces. Both structures have the same class of weak equivalences but different classes of fibrations and therefore of cofibrations. Using one of these structures, one obtains that the localized category is equivalent to the category of n-reduced CW-complexes with dimension less than or equal to m+1 and m-homotopy classes of cellular pointed maps. Using the other structure we see that the localized category is also equivalent to the homotopy category of (n-1)-connected (m+1)-coconnected CW-complexes.
publishDate 1997
dc.date.none.fl_str_mv 1997
dc.type.none.fl_str_mv info:eu-repo/semantics/article
Subtype: Article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://investigacion.unirioja.es/documentos/5bbc6a15b750603269e826b7
url https://investigacion.unirioja.es/documentos/5bbc6a15b750603269e826b7
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/pissn/1201-561X
Closed model categories for [n,m]-types, 1997, vol. 3, núm. 10, pág. 251-266
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:RIUR. Repositorio Institucional de la Universidad de La Rioja
instname:Universidad de La Rioja (UR)
instname_str Universidad de La Rioja (UR)
reponame_str RIUR. Repositorio Institucional de la Universidad de La Rioja
collection RIUR. Repositorio Institucional de la Universidad de La Rioja
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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