On the topological complexity of manifolds with abelian fundamental group

Detalhes bibliográficos
Autor(a) principal: Cohen, Daniel C.
Data de Publicação: 2021
Outros Autores: Vandembroucq, Lucile
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/87044
Resumo: We find conditions which ensure that the topological complexity of a closed manifold M with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on the topological complexity of spaces with small fundamen- tal group. Relaxing the commutativity condition on the fundamental group, we also generalize results of Dranishnikov on the Lusternik–Schnirelmann category of the cofibre of the diagonal map ∆ : M → M × M for nonorientable surfaces by establishing the nonmaximality of this invariant for a large class of manifolds.
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spelling On the topological complexity of manifolds with abelian fundamental groupLS-categoryTopological complexityLusternik-Schnirelmann categoryCiências Naturais::MatemáticasWe find conditions which ensure that the topological complexity of a closed manifold M with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on the topological complexity of spaces with small fundamen- tal group. Relaxing the commutativity condition on the fundamental group, we also generalize results of Dranishnikov on the Lusternik–Schnirelmann category of the cofibre of the diagonal map ∆ : M → M × M for nonorientable surfaces by establishing the nonmaximality of this invariant for a large class of manifolds.The second author is partially supported by Portuguese Funds through FCT – Fundação para a Ciência e a Tecnologia, within the projects UIDB/00013/2020 and UIDP/00013/2020.De GruyterUniversidade do MinhoCohen, Daniel C.Vandembroucq, Lucile20212021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/87044engCohen, D. C., & Vandembroucq, L. (2021, September 25). On the topological complexity of manifolds with abelian fundamental group. Forum Mathematicum. Walter de Gruyter GmbH. http://doi.org/10.1515/forum-2021-00940933-77411435-533710.1515/forum-2021-0094https://www.degruyter.com/document/doi/10.1515/forum-2021-0094/htmlinfo: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:RCAAP2023-10-28T01:19:00Zoai:repositorium.sdum.uminho.pt:1822/87044Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:25:58.605697Repositório 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 On the topological complexity of manifolds with abelian fundamental group
title On the topological complexity of manifolds with abelian fundamental group
spellingShingle On the topological complexity of manifolds with abelian fundamental group
Cohen, Daniel C.
LS-category
Topological complexity
Lusternik-Schnirelmann category
Ciências Naturais::Matemáticas
title_short On the topological complexity of manifolds with abelian fundamental group
title_full On the topological complexity of manifolds with abelian fundamental group
title_fullStr On the topological complexity of manifolds with abelian fundamental group
title_full_unstemmed On the topological complexity of manifolds with abelian fundamental group
title_sort On the topological complexity of manifolds with abelian fundamental group
author Cohen, Daniel C.
author_facet Cohen, Daniel C.
Vandembroucq, Lucile
author_role author
author2 Vandembroucq, Lucile
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Cohen, Daniel C.
Vandembroucq, Lucile
dc.subject.por.fl_str_mv LS-category
Topological complexity
Lusternik-Schnirelmann category
Ciências Naturais::Matemáticas
topic LS-category
Topological complexity
Lusternik-Schnirelmann category
Ciências Naturais::Matemáticas
description We find conditions which ensure that the topological complexity of a closed manifold M with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on the topological complexity of spaces with small fundamen- tal group. Relaxing the commutativity condition on the fundamental group, we also generalize results of Dranishnikov on the Lusternik–Schnirelmann category of the cofibre of the diagonal map ∆ : M → M × M for nonorientable surfaces by establishing the nonmaximality of this invariant for a large class of manifolds.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01T00:00:00Z
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 https://hdl.handle.net/1822/87044
url https://hdl.handle.net/1822/87044
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Cohen, D. C., & Vandembroucq, L. (2021, September 25). On the topological complexity of manifolds with abelian fundamental group. Forum Mathematicum. Walter de Gruyter GmbH. http://doi.org/10.1515/forum-2021-0094
0933-7741
1435-5337
10.1515/forum-2021-0094
https://www.degruyter.com/document/doi/10.1515/forum-2021-0094/html
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 De Gruyter
publisher.none.fl_str_mv De Gruyter
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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