Twisted Borel K-theory and isomorphisms between differential models of K-theory
Autor(a) principal: | |
---|---|
Data de Publicação: | 2022 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/16552 |
Resumo: | In this thesis we discuss some topics about twisted K-theory calculations and equivalences between a couple of differential extension models. We start with a mathematical review of models for twisted K-theory, differential extensions for the untwisted case, and Serre spectral sequences, in order to provide an explicit link between the differential extension of the untwisted and twisted cases, in addition to giving tools for the subsequent exploration of the twists that will be used. In the first part of this thesis we determine a formula up to group extensions for the twisted K-theory for a fiber bundle over the circle S^1 with fiber a compact manifold with respect to certain twists constructed from elements of the second cohomology group of the fiber. Later this case is generalized by allowing the base to be the classifying space of a finitely generated free group and the twisting will be given by a derivation of line bundles associated to the group and the fiber. This is accompanied by examples and we finally develop a spectral sequence where the previous formulas are framed. In the second part of the thesis, a topological equivalence is developed for the Freed-Lott and Carey-Mickelsson-Wang differential extension models. Additionally, we indicate a way to achieve the differential equivalence. |
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Posada, Alffer Gustavo HernandezRuffino, Fabio Ferrarihttp://lattes.cnpq.br/2512107188781159López, José María Cantarerohttp://lattes.cnpq.br/61278771384131120836788b-e51b-4d03-a7b5-99c8f85da7922022-08-31T20:07:43Z2022-08-31T20:07:43Z2022-07-04POSADA, Alffer Gustavo Hernandez. Twisted Borel K-theory and isomorphisms between differential models of K-theory. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16552.https://repositorio.ufscar.br/handle/ufscar/16552In this thesis we discuss some topics about twisted K-theory calculations and equivalences between a couple of differential extension models. We start with a mathematical review of models for twisted K-theory, differential extensions for the untwisted case, and Serre spectral sequences, in order to provide an explicit link between the differential extension of the untwisted and twisted cases, in addition to giving tools for the subsequent exploration of the twists that will be used. In the first part of this thesis we determine a formula up to group extensions for the twisted K-theory for a fiber bundle over the circle S^1 with fiber a compact manifold with respect to certain twists constructed from elements of the second cohomology group of the fiber. Later this case is generalized by allowing the base to be the classifying space of a finitely generated free group and the twisting will be given by a derivation of line bundles associated to the group and the fiber. This is accompanied by examples and we finally develop a spectral sequence where the previous formulas are framed. In the second part of the thesis, a topological equivalence is developed for the Freed-Lott and Carey-Mickelsson-Wang differential extension models. Additionally, we indicate a way to achieve the differential equivalence.Nesta tese discutimos alguns tópicos sobre cálculos da K-teoría torcida e equivalências entre dois modelos de extensão diferencial. Começamos com uma revisão matemática de modelos para a K-teoria torcida, extensões diferenciais para o caso não torcido e sequências espectrais de Serre e Atiyah-Hirzebruch, a fim de fornecer uma ligação explícita entre a extensão diferencial dos casos no torcidos e torcidos, além dar ferramentas para a exploração posterior dos torcimentos que serão utilizados. Na primeira parte desta tese, calculamos uma fórmula salvo extensões de grupo para a K-teoria torcida para um fibrado baseado no círculo S^1 com fibra uma variedade compacta e um torcimento dado em função de uma classe do segundo grupo de cohomología da fibra, posteriormente este caso é generalizado estendendo a base para o espaço classificatório de um grupo livre finitamente gerado e o torcimento será dado por derivações de feixes lineares associados ao grupo e à fibra, isto é acompanhado de exemplos para finalmente desenvolver um sequência espectral onde as fórmulas anteriores são enquadradas. Na segunda parte da tese, desenvolve-se uma equivalência topológica para os modelos de extensão diferencial de Freed-Lott e Carey-Mickelsson-Wang, além de indicar uma forma de alcançar a equivalência diferencial.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)88882.426776/2019-01engUniversidade 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/openAccessK-teoria topológicaOperadores de fredholmK-teoria torcidaK-teoria torcida de BorelK-teoria diferencialTopological K-TheoryFredholm operatorsTwisted K-TheoryTwisted Borel K-TheoryDifferential Twisted K-TheoryCIENCIAS EXATAS E DA TERRA::MATEMATICACIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIATwisted Borel K-theory and isomorphisms between differential models of K-theoryK-teoria de Borel torcida e isomorfimos entre modelos de K-teoria diferencialinfo: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/16552/3/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD53ORIGINALTese final Alffer.pdfTese final Alffer.pdfapplication/pdf1014835https://repositorio.ufscar.br/bitstream/ufscar/16552/1/Tese%20final%20Alffer.pdf8cd228c8939755412f417ecc01e4cbcfMD51Carta Comprovante Assinada.pdfCarta Comprovante Assinada.pdfCarta Comprovanteapplication/pdf636766https://repositorio.ufscar.br/bitstream/ufscar/16552/2/Carta%20Comprovante%20Assinada.pdfa50d231d46487199d357268e706f7f09MD52TEXTTese final Alffer.pdf.txtTese final Alffer.pdf.txtExtracted texttext/plain219909https://repositorio.ufscar.br/bitstream/ufscar/16552/4/Tese%20final%20Alffer.pdf.txtc62665ccf871b7cabdbb771af8cf95a3MD54Carta Comprovante Assinada.pdf.txtCarta Comprovante Assinada.pdf.txtExtracted texttext/plain1https://repositorio.ufscar.br/bitstream/ufscar/16552/6/Carta%20Comprovante%20Assinada.pdf.txt68b329da9893e34099c7d8ad5cb9c940MD56THUMBNAILTese final Alffer.pdf.jpgTese final Alffer.pdf.jpgIM Thumbnailimage/jpeg7691https://repositorio.ufscar.br/bitstream/ufscar/16552/5/Tese%20final%20Alffer.pdf.jpg00b62431257cb4b46930f992187288efMD55Carta Comprovante Assinada.pdf.jpgCarta Comprovante Assinada.pdf.jpgIM Thumbnailimage/jpeg12514https://repositorio.ufscar.br/bitstream/ufscar/16552/7/Carta%20Comprovante%20Assinada.pdf.jpg86de62ff286d479ce1b6898846a74e95MD57ufscar/165522023-09-18 18:32:17.649oai:repositorio.ufscar.br:ufscar/16552Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32:17Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
Twisted Borel K-theory and isomorphisms between differential models of K-theory |
dc.title.alternative.por.fl_str_mv |
K-teoria de Borel torcida e isomorfimos entre modelos de K-teoria diferencial |
title |
Twisted Borel K-theory and isomorphisms between differential models of K-theory |
spellingShingle |
Twisted Borel K-theory and isomorphisms between differential models of K-theory Posada, Alffer Gustavo Hernandez K-teoria topológica Operadores de fredholm K-teoria torcida K-teoria torcida de Borel K-teoria diferencial Topological K-Theory Fredholm operators Twisted K-Theory Twisted Borel K-Theory Differential Twisted K-Theory CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
title_short |
Twisted Borel K-theory and isomorphisms between differential models of K-theory |
title_full |
Twisted Borel K-theory and isomorphisms between differential models of K-theory |
title_fullStr |
Twisted Borel K-theory and isomorphisms between differential models of K-theory |
title_full_unstemmed |
Twisted Borel K-theory and isomorphisms between differential models of K-theory |
title_sort |
Twisted Borel K-theory and isomorphisms between differential models of K-theory |
author |
Posada, Alffer Gustavo Hernandez |
author_facet |
Posada, Alffer Gustavo Hernandez |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/6127877138413112 |
dc.contributor.author.fl_str_mv |
Posada, Alffer Gustavo Hernandez |
dc.contributor.advisor1.fl_str_mv |
Ruffino, Fabio Ferrari |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/2512107188781159 |
dc.contributor.advisor-co1.fl_str_mv |
López, José María Cantarero |
dc.contributor.authorID.fl_str_mv |
0836788b-e51b-4d03-a7b5-99c8f85da792 |
contributor_str_mv |
Ruffino, Fabio Ferrari López, José María Cantarero |
dc.subject.por.fl_str_mv |
K-teoria topológica Operadores de fredholm K-teoria torcida K-teoria torcida de Borel K-teoria diferencial |
topic |
K-teoria topológica Operadores de fredholm K-teoria torcida K-teoria torcida de Borel K-teoria diferencial Topological K-Theory Fredholm operators Twisted K-Theory Twisted Borel K-Theory Differential Twisted K-Theory CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
dc.subject.eng.fl_str_mv |
Topological K-Theory Fredholm operators Twisted K-Theory Twisted Borel K-Theory Differential Twisted K-Theory |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA |
description |
In this thesis we discuss some topics about twisted K-theory calculations and equivalences between a couple of differential extension models. We start with a mathematical review of models for twisted K-theory, differential extensions for the untwisted case, and Serre spectral sequences, in order to provide an explicit link between the differential extension of the untwisted and twisted cases, in addition to giving tools for the subsequent exploration of the twists that will be used. In the first part of this thesis we determine a formula up to group extensions for the twisted K-theory for a fiber bundle over the circle S^1 with fiber a compact manifold with respect to certain twists constructed from elements of the second cohomology group of the fiber. Later this case is generalized by allowing the base to be the classifying space of a finitely generated free group and the twisting will be given by a derivation of line bundles associated to the group and the fiber. This is accompanied by examples and we finally develop a spectral sequence where the previous formulas are framed. In the second part of the thesis, a topological equivalence is developed for the Freed-Lott and Carey-Mickelsson-Wang differential extension models. Additionally, we indicate a way to achieve the differential equivalence. |
publishDate |
2022 |
dc.date.accessioned.fl_str_mv |
2022-08-31T20:07:43Z |
dc.date.available.fl_str_mv |
2022-08-31T20:07:43Z |
dc.date.issued.fl_str_mv |
2022-07-04 |
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 |
POSADA, Alffer Gustavo Hernandez. Twisted Borel K-theory and isomorphisms between differential models of K-theory. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16552. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/16552 |
identifier_str_mv |
POSADA, Alffer Gustavo Hernandez. Twisted Borel K-theory and isomorphisms between differential models of K-theory. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16552. |
url |
https://repositorio.ufscar.br/handle/ufscar/16552 |
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 |
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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 |
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Universidade Federal de São Carlos (UFSCAR) |
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UFSCAR |
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UFSCAR |
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Repositório Institucional da UFSCAR |
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Repositório Institucional da UFSCAR |
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