Deficient and multiple points of maps into a manifold

Detalhes bibliográficos
Autor(a) principal: Goncalves, D. A. C. I. B. E. R. G. L.
Data de Publicação: 2020
Outros Autores: Monis, T. H. A. I. S. F. M. [UNESP], Spiez, S. T. A. N. I. S. L. A. W.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://hdl.handle.net/11449/237801
Resumo: The notion of Hopf's absolute degree is classically defined for mappings between manifolds of the same dimension, even when they are not necessarily orientable. In this paper, we extend such notion for mappings from more general spaces into manifolds. Once we have stablished a version of Hopf's absolute degree for certain maps f : X -> M, where M is a manifold but X need not be, we study the sets of deficient and multiple points of f. In case of the set of deficient points, we estimate its dimension. For multiple points, we study its density in X, and we also provide examples where its complement is dense.
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spelling Deficient and multiple points of maps into a manifoldThe notion of Hopf's absolute degree is classically defined for mappings between manifolds of the same dimension, even when they are not necessarily orientable. In this paper, we extend such notion for mappings from more general spaces into manifolds. Once we have stablished a version of Hopf's absolute degree for certain maps f : X -> M, where M is a manifold but X need not be, we study the sets of deficient and multiple points of f. In case of the set of deficient points, we estimate its dimension. For multiple points, we study its density in X, and we also provide examples where its complement is dense.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Sao Paulo, IME, Dept Math, Rua Matao 1010, BR-05508090 Sao Paulo, SP, BrazilSao Paulo State Univ Unesp, IGCE, Dept Math, Ave 24 A 1515, BR-13506900 Rio Claro, SP, BrazilPolish Acad Sci, IMPAN, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, PolandSao Paulo State Univ Unesp, IGCE, Dept Math, Ave 24 A 1515, BR-13506900 Rio Claro, SP, BrazilFAPESP: 2016/24707-4FAPESP: 2018/03550-5FAPESP: 2013/07936-1Univ HoustonUniversidade de São Paulo (USP)Universidade Estadual Paulista (UNESP)Polish Acad SciGoncalves, D. A. C. I. B. E. R. G. L.Monis, T. H. A. I. S. F. M. [UNESP]Spiez, S. T. A. N. I. S. L. A. W.2022-11-30T13:45:20Z2022-11-30T13:45:20Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1033-1052Houston Journal Of Mathematics. Houston: Univ Houston, v. 46, n. 4, p. 1033-1052, 2020.0362-1588http://hdl.handle.net/11449/237801WOS:000835337400010Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengHouston Journal Of Mathematicsinfo:eu-repo/semantics/openAccess2022-11-30T13:45:20Zoai:repositorio.unesp.br:11449/237801Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:32:38.345543Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Deficient and multiple points of maps into a manifold
title Deficient and multiple points of maps into a manifold
spellingShingle Deficient and multiple points of maps into a manifold
Goncalves, D. A. C. I. B. E. R. G. L.
title_short Deficient and multiple points of maps into a manifold
title_full Deficient and multiple points of maps into a manifold
title_fullStr Deficient and multiple points of maps into a manifold
title_full_unstemmed Deficient and multiple points of maps into a manifold
title_sort Deficient and multiple points of maps into a manifold
author Goncalves, D. A. C. I. B. E. R. G. L.
author_facet Goncalves, D. A. C. I. B. E. R. G. L.
Monis, T. H. A. I. S. F. M. [UNESP]
Spiez, S. T. A. N. I. S. L. A. W.
author_role author
author2 Monis, T. H. A. I. S. F. M. [UNESP]
Spiez, S. T. A. N. I. S. L. A. W.
author2_role author
author
dc.contributor.none.fl_str_mv Universidade de São Paulo (USP)
Universidade Estadual Paulista (UNESP)
Polish Acad Sci
dc.contributor.author.fl_str_mv Goncalves, D. A. C. I. B. E. R. G. L.
Monis, T. H. A. I. S. F. M. [UNESP]
Spiez, S. T. A. N. I. S. L. A. W.
description The notion of Hopf's absolute degree is classically defined for mappings between manifolds of the same dimension, even when they are not necessarily orientable. In this paper, we extend such notion for mappings from more general spaces into manifolds. Once we have stablished a version of Hopf's absolute degree for certain maps f : X -> M, where M is a manifold but X need not be, we study the sets of deficient and multiple points of f. In case of the set of deficient points, we estimate its dimension. For multiple points, we study its density in X, and we also provide examples where its complement is dense.
publishDate 2020
dc.date.none.fl_str_mv 2020-01-01
2022-11-30T13:45:20Z
2022-11-30T13:45:20Z
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 Houston Journal Of Mathematics. Houston: Univ Houston, v. 46, n. 4, p. 1033-1052, 2020.
0362-1588
http://hdl.handle.net/11449/237801
WOS:000835337400010
identifier_str_mv Houston Journal Of Mathematics. Houston: Univ Houston, v. 46, n. 4, p. 1033-1052, 2020.
0362-1588
WOS:000835337400010
url http://hdl.handle.net/11449/237801
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Houston Journal Of Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1033-1052
dc.publisher.none.fl_str_mv Univ Houston
publisher.none.fl_str_mv Univ Houston
dc.source.none.fl_str_mv Web of Science
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
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