Spaces which Invert Weak Homotopy Equivalences

Autores
Barmak, Jonathan Ariel
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
It is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f: [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f: [B, X] → [A, X] a bijection for every weak equivalence f? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible.
Fil: Barmak, Jonathan Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
HOMOTOPY TYPES
NON-HAUSDORFF SPACES
WEAK HOMOTOPY EQUIVALENCES
Nivel de accesibilidad
acceso embargado
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/88608
Acceder
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spelling Spaces which Invert Weak Homotopy EquivalencesBarmak, Jonathan ArielHOMOTOPY TYPESNON-HAUSDORFF SPACESWEAK HOMOTOPY EQUIVALENCEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1It is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f: [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f: [B, X] → [A, X] a bijection for every weak equivalence f? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible.Fil: Barmak, Jonathan Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaCambridge University Press2019-05info:eu-repo/date/embargoEnd/2020-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/88608Barmak, Jonathan Ariel; Spaces which Invert Weak Homotopy Equivalences; Cambridge University Press; Proceedings Of The Edinburgh Mathematical Society; 62; 2; 5-2019; 553-5580013-0915CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/spaces-which-invert-weak-homotopy-equivalences/DE7A5326298D8F5D6BE621DBCB110ED4info:eu-repo/semantics/altIdentifier/doi/10.1017/S0013091518000639info:eu-repo/semantics/embargoedAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:01:18Zoai:ri.conicet.gov.ar:11336/88608instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:01:19.08CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Spaces which Invert Weak Homotopy Equivalences
title Spaces which Invert Weak Homotopy Equivalences
spellingShingle Spaces which Invert Weak Homotopy Equivalences
Barmak, Jonathan Ariel
HOMOTOPY TYPES
NON-HAUSDORFF SPACES
WEAK HOMOTOPY EQUIVALENCES
title_short Spaces which Invert Weak Homotopy Equivalences
title_full Spaces which Invert Weak Homotopy Equivalences
title_fullStr Spaces which Invert Weak Homotopy Equivalences
title_full_unstemmed Spaces which Invert Weak Homotopy Equivalences
title_sort Spaces which Invert Weak Homotopy Equivalences
dc.creator.none.fl_str_mv Barmak, Jonathan Ariel
author Barmak, Jonathan Ariel
author_facet Barmak, Jonathan Ariel
author_role author
dc.subject.none.fl_str_mv HOMOTOPY TYPES
NON-HAUSDORFF SPACES
WEAK HOMOTOPY EQUIVALENCES
topic HOMOTOPY TYPES
NON-HAUSDORFF SPACES
WEAK HOMOTOPY EQUIVALENCES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv It is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f: [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f: [B, X] → [A, X] a bijection for every weak equivalence f? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible.
Fil: Barmak, Jonathan Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description It is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f: [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes have that property. Now, for which spaces X is f: [B, X] → [A, X] a bijection for every weak equivalence f? This question was considered by J. Strom and T. Goodwillie. In this note we prove that a non-empty space inverts weak equivalences if and only if it is contractible.
publishDate 2019
dc.date.none.fl_str_mv 2019-05
info:eu-repo/date/embargoEnd/2020-01-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/88608
Barmak, Jonathan Ariel; Spaces which Invert Weak Homotopy Equivalences; Cambridge University Press; Proceedings Of The Edinburgh Mathematical Society; 62; 2; 5-2019; 553-558
0013-0915
CONICET Digital
CONICET
url http://hdl.handle.net/11336/88608
identifier_str_mv Barmak, Jonathan Ariel; Spaces which Invert Weak Homotopy Equivalences; Cambridge University Press; Proceedings Of The Edinburgh Mathematical Society; 62; 2; 5-2019; 553-558
0013-0915
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/spaces-which-invert-weak-homotopy-equivalences/DE7A5326298D8F5D6BE621DBCB110ED4
info:eu-repo/semantics/altIdentifier/doi/10.1017/S0013091518000639
dc.rights.none.fl_str_mv info:eu-repo/semantics/embargoedAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv embargoedAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.48226

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