The differentiable chain functor is not homotopy equivalent to the continuous chain functor

Let $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equiv...

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Autores: Guillén Santos, Francisco, Navarro, Vicenç (Navarro Aznar), Pascual Gainza, Pere, Roig, Agustí
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2009
País:España
Recursos:Universidad de Barcelona
Repositório:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/34541
Acesso em linha:https://hdl.handle.net/2445/34541
Access Level:Acceso aberto
Palavra-chave:Topologia diferencial
Topologia algebraica
Àlgebra homològica
Differential topology
Algebraic topology
Homological algebra
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spelling The differentiable chain functor is not homotopy equivalent to the continuous chain functorGuillén Santos, FranciscoNavarro, Vicenç (Navarro Aznar)Pascual Gainza, PereRoig, AgustíTopologia diferencialTopologia algebraicaÀlgebra homològicaDifferential topologyAlgebraic topologyHomological algebraLet $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equivalence.Elsevier B.V.2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/34541Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: http://dx.doi.org/10.1016/j.topol.2008.09.005Topology and its Applications, 2009, vol. 156, num. 3, p. 658-660http://dx.doi.org/10.1016/j.topol.2008.09.005(c) Elsevier B.V., 2009info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/345412026-05-27T06:46:51Z
dc.title.none.fl_str_mv The differentiable chain functor is not homotopy equivalent to the continuous chain functor
title The differentiable chain functor is not homotopy equivalent to the continuous chain functor
spellingShingle The differentiable chain functor is not homotopy equivalent to the continuous chain functor
Guillén Santos, Francisco
Topologia diferencial
Topologia algebraica
Àlgebra homològica
Differential topology
Algebraic topology
Homological algebra
title_short The differentiable chain functor is not homotopy equivalent to the continuous chain functor
title_full The differentiable chain functor is not homotopy equivalent to the continuous chain functor
title_fullStr The differentiable chain functor is not homotopy equivalent to the continuous chain functor
title_full_unstemmed The differentiable chain functor is not homotopy equivalent to the continuous chain functor
title_sort The differentiable chain functor is not homotopy equivalent to the continuous chain functor
dc.creator.none.fl_str_mv Guillén Santos, Francisco
Navarro, Vicenç (Navarro Aznar)
Pascual Gainza, Pere
Roig, Agustí
author Guillén Santos, Francisco
author_facet Guillén Santos, Francisco
Navarro, Vicenç (Navarro Aznar)
Pascual Gainza, Pere
Roig, Agustí
author_role author
author2 Navarro, Vicenç (Navarro Aznar)
Pascual Gainza, Pere
Roig, Agustí
author2_role author
author
author
dc.subject.none.fl_str_mv Topologia diferencial
Topologia algebraica
Àlgebra homològica
Differential topology
Algebraic topology
Homological algebra
topic Topologia diferencial
Topologia algebraica
Àlgebra homològica
Differential topology
Algebraic topology
Homological algebra
description Let $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equivalence.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/34541
url https://hdl.handle.net/2445/34541
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: http://dx.doi.org/10.1016/j.topol.2008.09.005
Topology and its Applications, 2009, vol. 156, num. 3, p. 658-660
http://dx.doi.org/10.1016/j.topol.2008.09.005
dc.rights.none.fl_str_mv (c) Elsevier B.V., 2009
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Elsevier B.V., 2009
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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