Differential cohomology on maps of pairs and relative-parallel product
| Ano de defesa: | 2021 |
|---|---|
| Autor(a) principal: | |
| Orientador(a): |
Ruffino, Fabio Ferrari
 |
| Banca de defesa: | |
| 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: | |
| Palavras-chave em Inglês: | |
| Área do conhecimento CNPq: | |
| Link de acesso: | https://repositorio.ufscar.br/handle/20.500.14289/15183 |
Resumo: | In this thesis, we study three important topics. The first one provides an axiomatic framework to differential cohomology on maps of pairs of topological spaces, introducing the product between relative and parallel classes. The second one describes some concrete models of differential cohomology endowed with the relative-parallel product, showing that the axioms stated above are not empty. The third topic deals with the construction and the axiomatization of some meaningful versions of the Thom morphism and of the integration map, in which the parallel-relative product is essential. These definitions constitute the main application of this product, and they are at the same time the fundamental motivation that led us to consider it. |
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Nunez Maldonado, Juan CarlosRuffino, Fabio Ferrarihttp://lattes.cnpq.br/2512107188781159http://lattes.cnpq.br/071539578573630179158b36-80ab-4779-b7fe-ada25d5321562021-11-29T12:24:30Z2021-11-29T12:24:30Z2021-10-06NUNEZ MALDONADO, Juan Carlos. Differential cohomology on maps of pairs and relative-parallel product. 2021. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2021. Disponível em: https://repositorio.ufscar.br/handle/20.500.14289/15183.https://repositorio.ufscar.br/handle/20.500.14289/15183In this thesis, we study three important topics. The first one provides an axiomatic framework to differential cohomology on maps of pairs of topological spaces, introducing the product between relative and parallel classes. The second one describes some concrete models of differential cohomology endowed with the relative-parallel product, showing that the axioms stated above are not empty. The third topic deals with the construction and the axiomatization of some meaningful versions of the Thom morphism and of the integration map, in which the parallel-relative product is essential. These definitions constitute the main application of this product, and they are at the same time the fundamental motivation that led us to consider it.Nesta tese estudamos três questões importantes. A primeira consiste em fornecer um arcabouço axiomático para a cohomologia diferencial no contexto dos mapas de pares de espaços topológicos, introduzindo o produto entre classes relativas e classes paralelas. A segunda consiste em mostrar alguns modelos concretos de cohomologia diferencial com produto relativo-paralelo, para que os axiomas enunciados anteriormente não fiquem vazios. Enfim, a terceira questão consiste na construção e na axiomatização de algumas versões do morfismo de Thom e do mapa de integração, em que o produto paralelo-relativo é essencial. Estas definições constituem a aplicação principal do produto introduzido, sendo ao mesmo tempo a motivação principal que nos levou a considerá-lo.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 diferencialMapas de paresProduto relativo-paraleloK-teoria diferencialIntegração relativa e com suporte (verticalmente) compactoDifferential cohomologyMaps of pairsDifferential k-theoryRelative and (vertically)-compactly-supported integrationCIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIADifferential cohomology on maps of pairs and relative-parallel productCohomologia diferencial em mapas de pares e produto relativo-paraleloinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis600600756edf14-844a-440d-92bf-648d61ad3b16reponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALdissertação -Juan_Nunez.pdfdissertação -Juan_Nunez.pdfapplication/pdf951508https://repositorio.ufscar.br/bitstreams/1265b307-de11-404c-be6f-c8721f942edf/download0f1f6274536d7bdd2f9e8c64b16927b8MD51trueAnonymousREADCarta Comprovante.pdfCarta Comprovante.pdfapplication/pdf109813https://repositorio.ufscar.br/bitstreams/d1bf3e2f-ed9f-4f98-817c-36585e1863f6/download48bf638e67c116aa0fc8235540038ce9MD52falseCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstreams/599065b9-5657-40da-99d3-7f5ded9bd039/downloade39d27027a6cc9cb039ad269a5db8e34MD53falseAnonymousREADTEXTdissertação -Juan_Nunez.pdf.txtdissertação -Juan_Nunez.pdf.txtExtracted texttext/plain199700https://repositorio.ufscar.br/bitstreams/77683631-714d-4016-b42b-5791a50f8b47/download41459f32ddb067bf94123bf78c003598MD58falseAnonymousREADCarta Comprovante.pdf.txtCarta Comprovante.pdf.txtExtracted texttext/plain1https://repositorio.ufscar.br/bitstreams/ae7c3685-aa14-421f-afe4-77b60b87519e/download68b329da9893e34099c7d8ad5cb9c940MD510falseTHUMBNAILdissertação -Juan_Nunez.pdf.jpgdissertação -Juan_Nunez.pdf.jpgIM Thumbnailimage/jpeg5501https://repositorio.ufscar.br/bitstreams/de4d1e3e-568b-45fb-8f1d-47f42212eb80/download7c494ddd96a38b8873bf71331b93d89eMD59falseAnonymousREADCarta Comprovante.pdf.jpgCarta Comprovante.pdf.jpgIM Thumbnailimage/jpeg11783https://repositorio.ufscar.br/bitstreams/1d3c4187-e71e-4674-aa5b-d16c4dd94608/download082044ea0d8aa3ee116b62dcf84ad311MD511false20.500.14289/151832025-02-05 20:28:21.821http://creativecommons.org/licenses/by-nc-nd/3.0/br/Attribution-NonCommercial-NoDerivs 3.0 Brazilopen.accessoai:repositorio.ufscar.br:20.500.14289/15183https://repositorio.ufscar.brRepositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestrepositorio.sibi@ufscar.bropendoar:43222025-02-05T23:28:21Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
| dc.title.por.fl_str_mv |
Differential cohomology on maps of pairs and relative-parallel product |
| dc.title.alternative.eng.fl_str_mv |
Cohomologia diferencial em mapas de pares e produto relativo-paralelo |
| title |
Differential cohomology on maps of pairs and relative-parallel product |
| spellingShingle |
Differential cohomology on maps of pairs and relative-parallel product Nunez Maldonado, Juan Carlos Cohomologia diferencial Mapas de pares Produto relativo-paralelo K-teoria diferencial Integração relativa e com suporte (verticalmente) compacto Differential cohomology Maps of pairs Differential k-theory Relative and (vertically)-compactly-supported integration CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
| title_short |
Differential cohomology on maps of pairs and relative-parallel product |
| title_full |
Differential cohomology on maps of pairs and relative-parallel product |
| title_fullStr |
Differential cohomology on maps of pairs and relative-parallel product |
| title_full_unstemmed |
Differential cohomology on maps of pairs and relative-parallel product |
| title_sort |
Differential cohomology on maps of pairs and relative-parallel product |
| author |
Nunez Maldonado, Juan Carlos |
| author_facet |
Nunez Maldonado, Juan Carlos |
| author_role |
author |
| dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/0715395785736301 |
| dc.contributor.author.fl_str_mv |
Nunez Maldonado, Juan Carlos |
| 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 |
79158b36-80ab-4779-b7fe-ada25d532156 |
| contributor_str_mv |
Ruffino, Fabio Ferrari |
| dc.subject.por.fl_str_mv |
Cohomologia diferencial Mapas de pares Produto relativo-paralelo K-teoria diferencial Integração relativa e com suporte (verticalmente) compacto |
| topic |
Cohomologia diferencial Mapas de pares Produto relativo-paralelo K-teoria diferencial Integração relativa e com suporte (verticalmente) compacto Differential cohomology Maps of pairs Differential k-theory Relative and (vertically)-compactly-supported integration CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
| dc.subject.eng.fl_str_mv |
Differential cohomology Maps of pairs Differential k-theory Relative and (vertically)-compactly-supported integration |
| dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
| description |
In this thesis, we study three important topics. The first one provides an axiomatic framework to differential cohomology on maps of pairs of topological spaces, introducing the product between relative and parallel classes. The second one describes some concrete models of differential cohomology endowed with the relative-parallel product, showing that the axioms stated above are not empty. The third topic deals with the construction and the axiomatization of some meaningful versions of the Thom morphism and of the integration map, in which the parallel-relative product is essential. These definitions constitute the main application of this product, and they are at the same time the fundamental motivation that led us to consider it. |
| publishDate |
2021 |
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2021-11-29T12:24:30Z |
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2021-11-29T12:24:30Z |
| dc.date.issued.fl_str_mv |
2021-10-06 |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
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publishedVersion |
| dc.identifier.citation.fl_str_mv |
NUNEZ MALDONADO, Juan Carlos. Differential cohomology on maps of pairs and relative-parallel product. 2021. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2021. Disponível em: https://repositorio.ufscar.br/handle/20.500.14289/15183. |
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https://repositorio.ufscar.br/handle/20.500.14289/15183 |
| identifier_str_mv |
NUNEZ MALDONADO, Juan Carlos. Differential cohomology on maps of pairs and relative-parallel product. 2021. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2021. Disponível em: https://repositorio.ufscar.br/handle/20.500.14289/15183. |
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https://repositorio.ufscar.br/handle/20.500.14289/15183 |
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eng |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
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Universidade Federal de São Carlos Câmpus São Carlos |
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