Cohomologia de Alexander-Spanier e o teorema de Ballesteros

Detalhes bibliográficos
Ano de defesa: 2020
Autor(a) principal: Barbosa, Gabriel Santos
Orientador(a): Fernandes, Alexandre César Gurgel
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Teoria de cohomologia
Dualidade (Matemática)
Teorema de separação
Cohomology theory
Duality (Mathematics)
Separation theorem
Link de acesso: http://www.repositorio.ufc.br/handle/riufc/62805
Resumo: In the present work, we prove a more general version of Jordan’s Curve Theorem. Supposing that f : X ---> Y is a proper map, where X and Y are topological manifolds of dimensions n and n + 1 , respectively, and more hypotheses about the set of f ’s self intersections, we get a formula for the number of connected components of the complement of f(X) in Y . For this, we will present an alternative cohomology theory and prove its main properties.
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spelling Barbosa, Gabriel SantosFernandes, Alexandre César Gurgel2021-12-07T20:12:47Z2021-12-07T20:12:47Z2020-12-15BARBOSA, Gabriel Santos. Cohomologia de Alexander-Spanier e o teorema de Ballesteros. 2020. 41 f. Dissertação (Mestrado Acadêmico em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2020.http://www.repositorio.ufc.br/handle/riufc/62805In the present work, we prove a more general version of Jordan’s Curve Theorem. Supposing that f : X ---> Y is a proper map, where X and Y are topological manifolds of dimensions n and n + 1 , respectively, and more hypotheses about the set of f ’s self intersections, we get a formula for the number of connected components of the complement of f(X) in Y . For this, we will present an alternative cohomology theory and prove its main properties.No presente trabalho, provamos uma versão mais geral do Teorema da Curva de Jordan. Supondo que f : X ---> Y uma aplicação própria, onde X e Y são variedades topológicas n e n + 1 dimensionais, respectivamente, e mais poucas hipóteses sobre o conjunto de autointerseções de f , conseguimos uma fórmula para o número de componentes conexas do complementar de f(X) em Y . Para isso, apresentaremos uma teoria de cohomologia alternativa e provaremos suas principais propriedades.Teoria de cohomologiaDualidade (Matemática)Teorema de separaçãoCohomology theoryDuality (Mathematics)Separation theoremCohomologia de Alexander-Spanier e o teorema de BallesterosAlexander-Spanier cohomology and the Ballesteros theoreminfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessORIGINAL2020_dis_gsbarbosa.pdf2020_dis_gsbarbosa.pdfapplication/pdf412375http://repositorio.ufc.br/bitstream/riufc/62805/5/2020_dis_gsbarbosa.pdfd7df948822c8ff2a2519a16e58a7bdf0MD55LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/62805/4/license.txt8a4605be74aa9ea9d79846c1fba20a33MD54riufc/628052021-12-10 12:05:48.723oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2021-12-10T15:05:48Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Cohomologia de Alexander-Spanier e o teorema de Ballesteros
dc.title.en.pt_BR.fl_str_mv Alexander-Spanier cohomology and the Ballesteros theorem
title Cohomologia de Alexander-Spanier e o teorema de Ballesteros
spellingShingle Cohomologia de Alexander-Spanier e o teorema de Ballesteros
Barbosa, Gabriel Santos
Teoria de cohomologia
Dualidade (Matemática)
Teorema de separação
Cohomology theory
Duality (Mathematics)
Separation theorem
title_short Cohomologia de Alexander-Spanier e o teorema de Ballesteros
title_full Cohomologia de Alexander-Spanier e o teorema de Ballesteros
title_fullStr Cohomologia de Alexander-Spanier e o teorema de Ballesteros
title_full_unstemmed Cohomologia de Alexander-Spanier e o teorema de Ballesteros
title_sort Cohomologia de Alexander-Spanier e o teorema de Ballesteros
author Barbosa, Gabriel Santos
author_facet Barbosa, Gabriel Santos
author_role author
dc.contributor.author.fl_str_mv Barbosa, Gabriel Santos
dc.contributor.advisor1.fl_str_mv Fernandes, Alexandre César Gurgel
contributor_str_mv Fernandes, Alexandre César Gurgel
dc.subject.por.fl_str_mv Teoria de cohomologia
Dualidade (Matemática)
Teorema de separação
Cohomology theory
Duality (Mathematics)
Separation theorem
topic Teoria de cohomologia
Dualidade (Matemática)
Teorema de separação
Cohomology theory
Duality (Mathematics)
Separation theorem
description In the present work, we prove a more general version of Jordan’s Curve Theorem. Supposing that f : X ---> Y is a proper map, where X and Y are topological manifolds of dimensions n and n + 1 , respectively, and more hypotheses about the set of f ’s self intersections, we get a formula for the number of connected components of the complement of f(X) in Y . For this, we will present an alternative cohomology theory and prove its main properties.
publishDate 2020
dc.date.issued.fl_str_mv 2020-12-15
dc.date.accessioned.fl_str_mv 2021-12-07T20:12:47Z
dc.date.available.fl_str_mv 2021-12-07T20:12:47Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv BARBOSA, Gabriel Santos. Cohomologia de Alexander-Spanier e o teorema de Ballesteros. 2020. 41 f. Dissertação (Mestrado Acadêmico em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2020.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufc.br/handle/riufc/62805
identifier_str_mv BARBOSA, Gabriel Santos. Cohomologia de Alexander-Spanier e o teorema de Ballesteros. 2020. 41 f. Dissertação (Mestrado Acadêmico em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2020.
url http://www.repositorio.ufc.br/handle/riufc/62805
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
instacron:UFC
instname_str Universidade Federal do Ceará (UFC)
instacron_str UFC
institution UFC
reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
bitstream.url.fl_str_mv http://repositorio.ufc.br/bitstream/riufc/62805/5/2020_dis_gsbarbosa.pdf
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repository.name.fl_str_mv Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)
repository.mail.fl_str_mv bu@ufc.br || repositorio@ufc.br
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