A geometric interpretation of the Schützenberger group of a minimal subshift
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/44425 https://doi.org/10.1007/s11512-016-0233-7 |
Resumo: | The first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geometric considerations involving the Rauzy graphs of the subshift. Indeed, the group is shown to be isomorphic to the inverse limit of the profinite completions of the fundamental groups of the Rauzy graphs of the subshift. A further result involving geometric arguments on Rauzy graphs is a criterion for freeness of the profinite group of a minimal subshift based on the Return Theorem of Berthé et al. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
spelling |
A geometric interpretation of the Schützenberger group of a minimal subshiftThe first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geometric considerations involving the Rauzy graphs of the subshift. Indeed, the group is shown to be isomorphic to the inverse limit of the profinite completions of the fundamental groups of the Rauzy graphs of the subshift. A further result involving geometric arguments on Rauzy graphs is a criterion for freeness of the profinite group of a minimal subshift based on the Return Theorem of Berthé et al.International Press of Boston2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44425http://hdl.handle.net/10316/44425https://doi.org/10.1007/s11512-016-0233-7https://doi.org/10.1007/s11512-016-0233-7enghttps://projecteuclid.org/euclid.afm/1485802749Almeida, JorgeCosta, Alfredoinfo: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:RCAAP2021-06-29T10:02:55Zoai:estudogeral.uc.pt:10316/44425Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:23.604216Repositório 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 |
A geometric interpretation of the Schützenberger group of a minimal subshift |
title |
A geometric interpretation of the Schützenberger group of a minimal subshift |
spellingShingle |
A geometric interpretation of the Schützenberger group of a minimal subshift Almeida, Jorge |
title_short |
A geometric interpretation of the Schützenberger group of a minimal subshift |
title_full |
A geometric interpretation of the Schützenberger group of a minimal subshift |
title_fullStr |
A geometric interpretation of the Schützenberger group of a minimal subshift |
title_full_unstemmed |
A geometric interpretation of the Schützenberger group of a minimal subshift |
title_sort |
A geometric interpretation of the Schützenberger group of a minimal subshift |
author |
Almeida, Jorge |
author_facet |
Almeida, Jorge Costa, Alfredo |
author_role |
author |
author2 |
Costa, Alfredo |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Almeida, Jorge Costa, Alfredo |
description |
The first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profinite semigroup. In the case of minimal subshifts, the same group is shown in the present paper to also arise from geometric considerations involving the Rauzy graphs of the subshift. Indeed, the group is shown to be isomorphic to the inverse limit of the profinite completions of the fundamental groups of the Rauzy graphs of the subshift. A further result involving geometric arguments on Rauzy graphs is a criterion for freeness of the profinite group of a minimal subshift based on the Return Theorem of Berthé et al. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 |
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/10316/44425 http://hdl.handle.net/10316/44425 https://doi.org/10.1007/s11512-016-0233-7 https://doi.org/10.1007/s11512-016-0233-7 |
url |
http://hdl.handle.net/10316/44425 https://doi.org/10.1007/s11512-016-0233-7 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://projecteuclid.org/euclid.afm/1485802749 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
International Press of Boston |
publisher.none.fl_str_mv |
International Press of Boston |
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 |
repository.mail.fl_str_mv |
|
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1799133821103243264 |