TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES

Detalhes bibliográficos
Autor(a) principal: Batista, E. B.
Data de Publicação: 2022
Outros Autores: Costa, J. C.F. [UNESP], Meza-Sarmiento, I. S.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.5427/jsing.2022.25d
http://hdl.handle.net/11449/240686
Resumo: In this work we investigate the topological classification of circle-valued simple Morse-Bott functions on connected closed orientable surfaces, up to topological conjugacy. We provide a complete topological invariant, called the MB-Reeb graph. This invariant is based on the generalized Reeb graph and the topological type of singular level sets of these functions. The results presented here extend to those obtained by the authors in a previous work when the surface is the standard sphere.
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spelling TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACESMorse–Bott functionsReeb graphtopological equivalenceTopological invariantIn this work we investigate the topological classification of circle-valued simple Morse-Bott functions on connected closed orientable surfaces, up to topological conjugacy. We provide a complete topological invariant, called the MB-Reeb graph. This invariant is based on the generalized Reeb graph and the topological type of singular level sets of these functions. The results presented here extend to those obtained by the authors in a previous work when the surface is the standard sphere.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Centro de Ciências e Tecnologia Universidade Federal do Cariri, CEUniversidade Estadual Paulista (Unesp) Instituto de Biociências Letras e Ciências Exatas, Câmpus de São José do Rio PretoDepartamento de Matemática – UFSCar, Rod. Washington Luís, Km 235-C.P. 676, São PauloUniversidade Estadual Paulista (Unesp) Instituto de Biociências Letras e Ciências Exatas, Câmpus de São José do Rio PretoCAPES: 001Universidade Federal do CaririUniversidade Estadual Paulista (UNESP)Universidade Federal de São Carlos (UFSCar)Batista, E. B.Costa, J. C.F. [UNESP]Meza-Sarmiento, I. S.2023-03-01T20:28:19Z2023-03-01T20:28:19Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article78-89http://dx.doi.org/10.5427/jsing.2022.25dJournal of Singularities, v. 25, p. 78-89.1949-2006http://hdl.handle.net/11449/24068610.5427/jsing.2022.25d2-s2.0-85136302026Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Singularitiesinfo:eu-repo/semantics/openAccess2023-03-01T20:28:20Zoai:repositorio.unesp.br:11449/240686Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:24:45.839367Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES
title TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES
spellingShingle TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES
Batista, E. B.
Morse–Bott functions
Reeb graph
topological equivalence
Topological invariant
title_short TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES
title_full TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES
title_fullStr TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES
title_full_unstemmed TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES
title_sort TOPOLOGICAL CLASSIFICATION OF CIRCLE–VALUED SIMPLE MORSE–BOTT FUNCTIONS ON CLOSED ORIENTABLE SURFACES
author Batista, E. B.
author_facet Batista, E. B.
Costa, J. C.F. [UNESP]
Meza-Sarmiento, I. S.
author_role author
author2 Costa, J. C.F. [UNESP]
Meza-Sarmiento, I. S.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Federal do Cariri
Universidade Estadual Paulista (UNESP)
Universidade Federal de São Carlos (UFSCar)
dc.contributor.author.fl_str_mv Batista, E. B.
Costa, J. C.F. [UNESP]
Meza-Sarmiento, I. S.
dc.subject.por.fl_str_mv Morse–Bott functions
Reeb graph
topological equivalence
Topological invariant
topic Morse–Bott functions
Reeb graph
topological equivalence
Topological invariant
description In this work we investigate the topological classification of circle-valued simple Morse-Bott functions on connected closed orientable surfaces, up to topological conjugacy. We provide a complete topological invariant, called the MB-Reeb graph. This invariant is based on the generalized Reeb graph and the topological type of singular level sets of these functions. The results presented here extend to those obtained by the authors in a previous work when the surface is the standard sphere.
publishDate 2022
dc.date.none.fl_str_mv 2022-01-01
2023-03-01T20:28:19Z
2023-03-01T20:28:19Z
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://dx.doi.org/10.5427/jsing.2022.25d
Journal of Singularities, v. 25, p. 78-89.
1949-2006
http://hdl.handle.net/11449/240686
10.5427/jsing.2022.25d
2-s2.0-85136302026
url http://dx.doi.org/10.5427/jsing.2022.25d
http://hdl.handle.net/11449/240686
identifier_str_mv Journal of Singularities, v. 25, p. 78-89.
1949-2006
10.5427/jsing.2022.25d
2-s2.0-85136302026
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Singularities
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 78-89
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129518329659392

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