Differential cohomology on maps of pairs and relative-parallel product
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/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. |
id |
SCAR_bbd29055d9edda917e5e5ec9d14f38bb |
---|---|
oai_identifier_str |
oai:repositorio.ufscar.br:ufscar/15183 |
network_acronym_str |
SCAR |
network_name_str |
Repositório Institucional da UFSCAR |
repository_id_str |
4322 |
spelling |
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/ufscar/15183.https://repositorio.ufscar.br/handle/ufscar/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:UFSCARCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstream/ufscar/15183/3/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD53ORIGINALdissertação -Juan_Nunez.pdfdissertação -Juan_Nunez.pdfapplication/pdf951508https://repositorio.ufscar.br/bitstream/ufscar/15183/1/disserta%c3%a7%c3%a3o%20-Juan_Nunez.pdf0f1f6274536d7bdd2f9e8c64b16927b8MD51Carta Comprovante.pdfCarta Comprovante.pdfapplication/pdf109813https://repositorio.ufscar.br/bitstream/ufscar/15183/2/Carta%20Comprovante.pdf48bf638e67c116aa0fc8235540038ce9MD52TEXTdissertação -Juan_Nunez.pdf.txtdissertação -Juan_Nunez.pdf.txtExtracted texttext/plain199700https://repositorio.ufscar.br/bitstream/ufscar/15183/4/disserta%c3%a7%c3%a3o%20-Juan_Nunez.pdf.txt41459f32ddb067bf94123bf78c003598MD54Carta Comprovante.pdf.txtCarta Comprovante.pdf.txtExtracted texttext/plain1https://repositorio.ufscar.br/bitstream/ufscar/15183/6/Carta%20Comprovante.pdf.txt68b329da9893e34099c7d8ad5cb9c940MD56THUMBNAILdissertação -Juan_Nunez.pdf.jpgdissertação -Juan_Nunez.pdf.jpgIM Thumbnailimage/jpeg5497https://repositorio.ufscar.br/bitstream/ufscar/15183/5/disserta%c3%a7%c3%a3o%20-Juan_Nunez.pdf.jpgc031c7c26165b41970382341f4937d7fMD55Carta Comprovante.pdf.jpgCarta Comprovante.pdf.jpgIM Thumbnailimage/jpeg11769https://repositorio.ufscar.br/bitstream/ufscar/15183/7/Carta%20Comprovante.pdf.jpgd9349bff023ca2a5a0f5c493f5ee3ce8MD57ufscar/151832023-09-18 18:32:23.146oai:repositorio.ufscar.br:ufscar/15183Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32:23Repositório 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 |
dc.date.accessioned.fl_str_mv |
2021-11-29T12:24:30Z |
dc.date.available.fl_str_mv |
2021-11-29T12:24:30Z |
dc.date.issued.fl_str_mv |
2021-10-06 |
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 |
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/ufscar/15183. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/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/ufscar/15183. |
url |
https://repositorio.ufscar.br/handle/ufscar/15183 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.confidence.fl_str_mv |
600 600 |
dc.relation.authority.fl_str_mv |
756edf14-844a-440d-92bf-648d61ad3b16 |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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 |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFSCAR instname:Universidade Federal de São Carlos (UFSCAR) instacron:UFSCAR |
instname_str |
Universidade Federal de São Carlos (UFSCAR) |
instacron_str |
UFSCAR |
institution |
UFSCAR |
reponame_str |
Repositório Institucional da UFSCAR |
collection |
Repositório Institucional da UFSCAR |
bitstream.url.fl_str_mv |
https://repositorio.ufscar.br/bitstream/ufscar/15183/3/license_rdf https://repositorio.ufscar.br/bitstream/ufscar/15183/1/disserta%c3%a7%c3%a3o%20-Juan_Nunez.pdf https://repositorio.ufscar.br/bitstream/ufscar/15183/2/Carta%20Comprovante.pdf https://repositorio.ufscar.br/bitstream/ufscar/15183/4/disserta%c3%a7%c3%a3o%20-Juan_Nunez.pdf.txt https://repositorio.ufscar.br/bitstream/ufscar/15183/6/Carta%20Comprovante.pdf.txt https://repositorio.ufscar.br/bitstream/ufscar/15183/5/disserta%c3%a7%c3%a3o%20-Juan_Nunez.pdf.jpg https://repositorio.ufscar.br/bitstream/ufscar/15183/7/Carta%20Comprovante.pdf.jpg |
bitstream.checksum.fl_str_mv |
e39d27027a6cc9cb039ad269a5db8e34 0f1f6274536d7bdd2f9e8c64b16927b8 48bf638e67c116aa0fc8235540038ce9 41459f32ddb067bf94123bf78c003598 68b329da9893e34099c7d8ad5cb9c940 c031c7c26165b41970382341f4937d7f d9349bff023ca2a5a0f5c493f5ee3ce8 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR) |
repository.mail.fl_str_mv |
|
_version_ |
1802136398303592448 |