Compactly-supported and relative integration in differential cohomology

Detalhes bibliográficos
Ano de defesa: 2022
Autor(a) principal: Barbosa, Brenno Gustavo
Orientador(a): Ruffino, Fabio Ferrari lattes
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: eng
Instituição de defesa: Universidade Federal de São Carlos
Câmpus São Carlos
Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Cohomologia diferencial
Integração diferencial
Topologia algébrica
Geometria diferencial
Palavras-chave em Inglês:
Differential cohomology
Differential integration
Algebraic topology
Differential geometry
Área do conhecimento CNPq:
CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA
Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/16247
Resumo: In this work, we have constructed more general versions of differential integration maps in differential cohomology theories. Among the obtained versions we can mention the integration with compact supports, the integration with vertically compact supports and their relative versions. To obtain these maps, it was necessary to construct a special product between parallel and relative differential classes and to extend differential cohomology theories to a category of sequences of manifolds.
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spelling Barbosa, Brenno GustavoRuffino, Fabio Ferrarihttp://lattes.cnpq.br/2512107188781159http://lattes.cnpq.br/44602668110840973ff55d68-2839-4c8f-af2f-46fc3543e0db2022-06-08T16:59:47Z2022-06-08T16:59:47Z2022-04-11BARBOSA, Brenno Gustavo. Compactly-supported and relative integration in differential cohomology. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/20.500.14289/16247.https://repositorio.ufscar.br/handle/20.500.14289/16247In this work, we have constructed more general versions of differential integration maps in differential cohomology theories. Among the obtained versions we can mention the integration with compact supports, the integration with vertically compact supports and their relative versions. To obtain these maps, it was necessary to construct a special product between parallel and relative differential classes and to extend differential cohomology theories to a category of sequences of manifolds.Neste trabalho, foram construídas versões mais gerais da integração diferencial em teorias de cohomologia diferencial. Dentre as versões obtidas podemos citar a integração com suporte compacto, a integração com suporte verticalmente compacto e suas versões relativas. Para obter estes mapas, foi necessário construir um produto especial entre classes diferenciais paralelas e relativas e estender a teoria de cohomologia diferencial a uma categoria de sequencias de variedades.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)CAPES: Código de financiamento 001engUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Matemática - PPGMUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessCohomologia diferencialIntegração diferencialTopologia algébricaGeometria diferencialDifferential cohomologyDifferential integrationAlgebraic topologyDifferential geometryCIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIACompactly-supported and relative integration in differential cohomologyIntegração com suporte compacto e relativa em cohomologia diferencialinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis600600756edf14-844a-440d-92bf-648d61ad3b16reponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTeseBrenno.pdfTeseBrenno.pdfapplication/pdf2363658https://repositorio.ufscar.br/bitstreams/2ac6a571-c367-482c-80f3-6c369d30ccb5/download45326982bdff6d5203939d0cb1928c09MD51trueAnonymousREADCarta Comprovante.pdfCarta Comprovante.pdfCarta comprovanteapplication/pdf340304https://repositorio.ufscar.br/bitstreams/8ac657ab-22f9-4660-8448-c9ea2fa6568b/download85eae6a2de28e3c68b44e99629a5d69fMD53falseCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstreams/5bf33484-77aa-4ca2-a8ef-28e33345bfef/downloade39d27027a6cc9cb039ad269a5db8e34MD54falseAnonymousREADTEXTTeseBrenno.pdf.txtTeseBrenno.pdf.txtExtracted texttext/plain477213https://repositorio.ufscar.br/bitstreams/7e4961f3-4744-4de4-ae87-ab756c244c71/downloadf1dc39d7441e091e290629854614738dMD59falseAnonymousREADCarta Comprovante.pdf.txtCarta Comprovante.pdf.txtExtracted texttext/plain1318https://repositorio.ufscar.br/bitstreams/7527358b-e3d0-4728-acf4-a9728014b408/download22f980e24563fc3cf6d2389c4e751de9MD511falseTHUMBNAILTeseBrenno.pdf.jpgTeseBrenno.pdf.jpgIM Thumbnailimage/jpeg4120https://repositorio.ufscar.br/bitstreams/d6a99a4a-36eb-4889-ad90-b764f90b3ec4/download77c51163415aabaa90d4ba06862e86a8MD510falseAnonymousREADCarta Comprovante.pdf.jpgCarta Comprovante.pdf.jpgIM Thumbnailimage/jpeg13116https://repositorio.ufscar.br/bitstreams/8f2d2789-6d1c-4e64-aa3a-810d89515637/downloadb3a63a59c8e6017aff7a6994115d0d05MD512false20.500.14289/162472025-02-05 21:28:59.217http://creativecommons.org/licenses/by-nc-nd/3.0/br/Attribution-NonCommercial-NoDerivs 3.0 Brazilopen.accessoai:repositorio.ufscar.br:20.500.14289/16247https://repositorio.ufscar.brRepositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestrepositorio.sibi@ufscar.bropendoar:43222025-02-06T00:28:59Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false
dc.title.eng.fl_str_mv Compactly-supported and relative integration in differential cohomology
dc.title.alternative.por.fl_str_mv Integração com suporte compacto e relativa em cohomologia diferencial
title Compactly-supported and relative integration in differential cohomology
spellingShingle Compactly-supported and relative integration in differential cohomology
Barbosa, Brenno Gustavo
Cohomologia diferencial
Integração diferencial
Topologia algébrica
Geometria diferencial
Differential cohomology
Differential integration
Algebraic topology
Differential geometry
CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA
title_short Compactly-supported and relative integration in differential cohomology
title_full Compactly-supported and relative integration in differential cohomology
title_fullStr Compactly-supported and relative integration in differential cohomology
title_full_unstemmed Compactly-supported and relative integration in differential cohomology
title_sort Compactly-supported and relative integration in differential cohomology
author Barbosa, Brenno Gustavo
author_facet Barbosa, Brenno Gustavo
author_role author
dc.contributor.authorlattes.por.fl_str_mv http://lattes.cnpq.br/4460266811084097
dc.contributor.author.fl_str_mv Barbosa, Brenno Gustavo
dc.contributor.advisor1.fl_str_mv Ruffino, Fabio Ferrari
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/2512107188781159
dc.contributor.authorID.fl_str_mv 3ff55d68-2839-4c8f-af2f-46fc3543e0db
contributor_str_mv Ruffino, Fabio Ferrari
dc.subject.por.fl_str_mv Cohomologia diferencial
Integração diferencial
Topologia algébrica
Geometria diferencial
topic Cohomologia diferencial
Integração diferencial
Topologia algébrica
Geometria diferencial
Differential cohomology
Differential integration
Algebraic topology
Differential geometry
CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA
dc.subject.eng.fl_str_mv Differential cohomology
Differential integration
Algebraic topology
Differential geometry
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA
description In this work, we have constructed more general versions of differential integration maps in differential cohomology theories. Among the obtained versions we can mention the integration with compact supports, the integration with vertically compact supports and their relative versions. To obtain these maps, it was necessary to construct a special product between parallel and relative differential classes and to extend differential cohomology theories to a category of sequences of manifolds.
publishDate 2022
dc.date.accessioned.fl_str_mv 2022-06-08T16:59:47Z
dc.date.available.fl_str_mv 2022-06-08T16:59:47Z
dc.date.issued.fl_str_mv 2022-04-11
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv BARBOSA, Brenno Gustavo. Compactly-supported and relative integration in differential cohomology. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/20.500.14289/16247.
dc.identifier.uri.fl_str_mv https://repositorio.ufscar.br/handle/20.500.14289/16247
identifier_str_mv BARBOSA, Brenno Gustavo. Compactly-supported and relative integration in differential cohomology. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/20.500.14289/16247.
url https://repositorio.ufscar.br/handle/20.500.14289/16247
dc.language.iso.fl_str_mv eng
language eng
dc.relation.confidence.fl_str_mv 600
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dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
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rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática - PPGM
dc.publisher.initials.fl_str_mv UFSCar
publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
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