Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes

Detalhes bibliográficos
Autor(a) principal: González, Jesús
Data de Publicação: 2018
Outros Autores: Grant, Mark, Vandembroucq, Lucile
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/69066
Resumo: Let X be a two-cell complex with attaching map α : S q → S p , and let C_X be the cofiber of the diagonal inclusion X → X × X. It is shown that the topological complexity (TC ) of X agrees with the Lusternik-Schnirelmann category (cat ) of C_X in the (almost stable) range q ≤ 2p − 1. In addition, the equality TC (X) = cat (C_X ) is proved in the (strict) metastable range 2p − 1 < q ≤ 3(p − 1) under fairly mild conditions by making use of the Hopf invariant techniques recently developed by the authors in their study of the sectional category of arbitrary maps.
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spelling Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexesLusternik-Schnirelmann categoryTopological complexityGeneralized Hopf invariantsTwo-cell complexFiberwise joingeneralized-Hopf invariantCiências Naturais::MatemáticasScience & TechnologyLet X be a two-cell complex with attaching map α : S q → S p , and let C_X be the cofiber of the diagonal inclusion X → X × X. It is shown that the topological complexity (TC ) of X agrees with the Lusternik-Schnirelmann category (cat ) of C_X in the (almost stable) range q ≤ 2p − 1. In addition, the equality TC (X) = cat (C_X ) is proved in the (strict) metastable range 2p − 1 < q ≤ 3(p − 1) under fairly mild conditions by making use of the Hopf invariant techniques recently developed by the authors in their study of the sectional category of arbitrary maps.JG was partially supported by Conacyt Research Grant 221221. LV was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the “Fundação para a Ciência e a Tecnologia”, through the Project UID/MAT/0013/2013.American Mathematical SocietyUniversidade do MinhoGonzález, JesúsGrant, MarkVandembroucq, Lucile20182018-01-01T00:00:00Zconference paperinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/1822/69066engGonzález , J , Grant , M & Vandembroucq (2018) , Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes . in M Grant , G Lupton & L Vandembroucq (eds) , Topological complexity and related topics . vol. 702 , Contemporary Mathematics , American Mathematical Society , pp. 133-150978-1-4704-3436-60271-413210.1090/conm/702/14109978-1-4704-4405-1https://www.ams.org/books/conm/702/info: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:RCAAP2024-05-11T07:23:38Zoai:repositorium.sdum.uminho.pt:1822/69066Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T07:23:38Repositório 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 Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
title Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
spellingShingle Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
González, Jesús
Lusternik-Schnirelmann category
Topological complexity
Generalized Hopf invariants
Two-cell complex
Fiberwise join
generalized-Hopf invariant
Ciências Naturais::Matemáticas
Science & Technology
title_short Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
title_full Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
title_fullStr Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
title_full_unstemmed Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
title_sort Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes
author González, Jesús
author_facet González, Jesús
Grant, Mark
Vandembroucq, Lucile
author_role author
author2 Grant, Mark
Vandembroucq, Lucile
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv González, Jesús
Grant, Mark
Vandembroucq, Lucile
dc.subject.por.fl_str_mv Lusternik-Schnirelmann category
Topological complexity
Generalized Hopf invariants
Two-cell complex
Fiberwise join
generalized-Hopf invariant
Ciências Naturais::Matemáticas
Science & Technology
topic Lusternik-Schnirelmann category
Topological complexity
Generalized Hopf invariants
Two-cell complex
Fiberwise join
generalized-Hopf invariant
Ciências Naturais::Matemáticas
Science & Technology
description Let X be a two-cell complex with attaching map α : S q → S p , and let C_X be the cofiber of the diagonal inclusion X → X × X. It is shown that the topological complexity (TC ) of X agrees with the Lusternik-Schnirelmann category (cat ) of C_X in the (almost stable) range q ≤ 2p − 1. In addition, the equality TC (X) = cat (C_X ) is proved in the (strict) metastable range 2p − 1 < q ≤ 3(p − 1) under fairly mild conditions by making use of the Hopf invariant techniques recently developed by the authors in their study of the sectional category of arbitrary maps.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01T00:00:00Z
dc.type.driver.fl_str_mv conference paper
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/69066
url http://hdl.handle.net/1822/69066
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv González , J , Grant , M & Vandembroucq (2018) , Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes . in M Grant , G Lupton & L Vandembroucq (eds) , Topological complexity and related topics . vol. 702 , Contemporary Mathematics , American Mathematical Society , pp. 133-150
978-1-4704-3436-6
0271-4132
10.1090/conm/702/14109
978-1-4704-4405-1
https://www.ams.org/books/conm/702/
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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 mluisa.alvim@gmail.com
_version_ 1817545301272035328

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