Sullivan constructions for transitive Lie algebroids - smooth case
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Data de Publicação: | 2017 |
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Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/50662 |
Resumo: | Let M be a smooth manifold, smoothly triangulated by a simplicial complex K, and A a transitive Lie algebroid on M. A piecewise smooth form on A is a family of smooth forms, each one defined on the restriction of A to a simplex of K, satisfying the compatibility condition concerning the restrictions of the simplex to the faces of that simplex. The set of all piecewise smooth forms on A is a cochain algebra. One has a natural morphism from the cochain algebra of smooth forms on A to the cochain algebra of piecewise smooth forms on A given by restriction of a smooth form defined on A to a smooth form defined on the restriction of A to each simplex of K. In this paper, we prove that, for triangulated compact manifolds, the cohomology of this construction is isomorphic to the Lie algebroid cohomology of A, in which the isomorphism is induced by the restriction mapping. |
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Sullivan constructions for transitive Lie algebroids - smooth caseLie algebroid cohomologyPiecewise smooth cohomology,Rham-Sullivan theoremCiências Naturais::MatemáticasLet M be a smooth manifold, smoothly triangulated by a simplicial complex K, and A a transitive Lie algebroid on M. A piecewise smooth form on A is a family of smooth forms, each one defined on the restriction of A to a simplex of K, satisfying the compatibility condition concerning the restrictions of the simplex to the faces of that simplex. The set of all piecewise smooth forms on A is a cochain algebra. One has a natural morphism from the cochain algebra of smooth forms on A to the cochain algebra of piecewise smooth forms on A given by restriction of a smooth form defined on A to a smooth form defined on the restriction of A to each simplex of K. In this paper, we prove that, for triangulated compact manifolds, the cohomology of this construction is isomorphic to the Lie algebroid cohomology of A, in which the isomorphism is induced by the restriction mapping.MICINN, Grant MTM2014-56950-Pinfo:eu-repo/semantics/submittedVersionUniversidade do MinhoMishchenko, Aleksandr S.Oliveira, Jose R.2017-092017-09-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/50662enghttps://arxiv.org/abs/1709.07494info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:35:49ZPortal AgregadorONG |
dc.title.none.fl_str_mv |
Sullivan constructions for transitive Lie algebroids - smooth case |
title |
Sullivan constructions for transitive Lie algebroids - smooth case |
spellingShingle |
Sullivan constructions for transitive Lie algebroids - smooth case Mishchenko, Aleksandr S. Lie algebroid cohomology Piecewise smooth cohomology, Rham-Sullivan theorem Ciências Naturais::Matemáticas |
title_short |
Sullivan constructions for transitive Lie algebroids - smooth case |
title_full |
Sullivan constructions for transitive Lie algebroids - smooth case |
title_fullStr |
Sullivan constructions for transitive Lie algebroids - smooth case |
title_full_unstemmed |
Sullivan constructions for transitive Lie algebroids - smooth case |
title_sort |
Sullivan constructions for transitive Lie algebroids - smooth case |
author |
Mishchenko, Aleksandr S. |
author_facet |
Mishchenko, Aleksandr S. Oliveira, Jose R. |
author_role |
author |
author2 |
Oliveira, Jose R. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Mishchenko, Aleksandr S. Oliveira, Jose R. |
dc.subject.por.fl_str_mv |
Lie algebroid cohomology Piecewise smooth cohomology, Rham-Sullivan theorem Ciências Naturais::Matemáticas |
topic |
Lie algebroid cohomology Piecewise smooth cohomology, Rham-Sullivan theorem Ciências Naturais::Matemáticas |
description |
Let M be a smooth manifold, smoothly triangulated by a simplicial complex K, and A a transitive Lie algebroid on M. A piecewise smooth form on A is a family of smooth forms, each one defined on the restriction of A to a simplex of K, satisfying the compatibility condition concerning the restrictions of the simplex to the faces of that simplex. The set of all piecewise smooth forms on A is a cochain algebra. One has a natural morphism from the cochain algebra of smooth forms on A to the cochain algebra of piecewise smooth forms on A given by restriction of a smooth form defined on A to a smooth form defined on the restriction of A to each simplex of K. In this paper, we prove that, for triangulated compact manifolds, the cohomology of this construction is isomorphic to the Lie algebroid cohomology of A, in which the isomorphism is induced by the restriction mapping. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-09 2017-09-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/50662 |
url |
http://hdl.handle.net/1822/50662 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://arxiv.org/abs/1709.07494 |
dc.rights.driver.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:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
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repository.mail.fl_str_mv |
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1777303795590496256 |