Definably compact abelian groups

Detalhes bibliográficos
Autor(a) principal: Edmundo, Mário
Data de Publicação: 2004
Outros Autores: Otero, Margarita
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/2760
Resumo: Let M be an o-minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n-dimensional group definable in M. We show the following: the o-minimal fundamental group of G is isomorphic to ℤ^n; for each k>0, the k-torsion subgroup of G is isomorphic to (ℤ/kℤ)^n, and the o-minimal cohomology algebra over ℚ of G is isomorphic to the exterior algebra over ℚ with n generators of degree one.
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spelling Definably compact abelian groupsO-minimal structuresDefinable groupsTorsion pointsLet M be an o-minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n-dimensional group definable in M. We show the following: the o-minimal fundamental group of G is isomorphic to ℤ^n; for each k>0, the k-torsion subgroup of G is isomorphic to (ℤ/kℤ)^n, and the o-minimal cohomology algebra over ℚ of G is isomorphic to the exterior algebra over ℚ with n generators of degree one.World ScientificRepositório AbertoEdmundo, MárioOtero, Margarita2014-01-08T12:11:10Z2004-122004-12-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/2760engEdmundo, Mário Jorge; Otero, Margarita - Definably compact abelian groups. "Journal of Mathematical Logic" [Em linha]. ISSN I793-6691 (Print) 0219-0613 (Online). Vol. 4, nº 2 (Dez. 2004), p. 1-210219-0613info: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:RCAAP2023-11-16T15:16:42Zoai:repositorioaberto.uab.pt:10400.2/2760Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:44:09.061726Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Definably compact abelian groups
title Definably compact abelian groups
spellingShingle Definably compact abelian groups
Edmundo, Mário
O-minimal structures
Definable groups
Torsion points
title_short Definably compact abelian groups
title_full Definably compact abelian groups
title_fullStr Definably compact abelian groups
title_full_unstemmed Definably compact abelian groups
title_sort Definably compact abelian groups
author Edmundo, Mário
author_facet Edmundo, Mário
Otero, Margarita
author_role author
author2 Otero, Margarita
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Edmundo, Mário
Otero, Margarita
dc.subject.por.fl_str_mv O-minimal structures
Definable groups
Torsion points
topic O-minimal structures
Definable groups
Torsion points
description Let M be an o-minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n-dimensional group definable in M. We show the following: the o-minimal fundamental group of G is isomorphic to ℤ^n; for each k>0, the k-torsion subgroup of G is isomorphic to (ℤ/kℤ)^n, and the o-minimal cohomology algebra over ℚ of G is isomorphic to the exterior algebra over ℚ with n generators of degree one.
publishDate 2004
dc.date.none.fl_str_mv 2004-12
2004-12-01T00:00:00Z
2014-01-08T12:11:10Z
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/10400.2/2760
url http://hdl.handle.net/10400.2/2760
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Edmundo, Mário Jorge; Otero, Margarita - Definably compact abelian groups. "Journal of Mathematical Logic" [Em linha]. ISSN I793-6691 (Print) 0219-0613 (Online). Vol. 4, nº 2 (Dez. 2004), p. 1-21
0219-0613
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.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
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 Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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