Categorification of Chern-Weil theory and equivariant cohomology

dc.contributor.advisorQuintero Vélez, Alexander
dc.contributor.advisorArias Abad, Camilo
dc.contributor.authorPineda Montoya, Santiago
dc.contributor.orcidArias Abad, Camilo [0000-0003-3624-9396]spa
dc.date.accessioned2023-02-07T14:02:58Z
dc.date.available2023-02-07T14:02:58Z
dc.date.issued2022-06-28
dc.descriptiondiagramasspa
dc.description.abstractEsta tesis contempla la generalización de resultados de geomtría diferencial clásica en el contexto de los sistemas locales homotópicos. En particular, se realiza la construcción del homomorfismo de Chern-Weil y el teorema equivariante de de Rham en el contexto de las categorias diferenciales graduadas conformadas por los sistemas locales homotópicos. (Texto tomado de la fuente)spa
dc.description.abstractLet G be a compact connected Lie group acting on a smooth manifold M. We show that the DG categories Loc∞(BG) and Loc∞(MG) of ∞-local systems on the classifying space of G and the homotopy quotient of M, respectively, can be described infinitesimally as the categories InfLoc∞(g) of basic g-L∞ spaces and InfLoc∞(g,M) of g graded G-equivariant vector bundles, respectively. Moreover, we show that, given a principal bundle π : P → X with structure group G and any connection θ on P, there are DG functors C Wθ : InfLoc∞(g) −→ Loc∞(X), and Cθ : InfLoc∞(g,M) −→ Loc∞((P× M)/G), that corresponds to the pullback functor by the classifying map of P. An A∞-natural isomorphism relates the functors associated with different connections. This construction categorizes the ChernWeil homomorphism, which is recovered by applying the functor C Wθ to the endomorphisms of the constant local system. Finally, we obtain a categorification of the equivariant de Rham theorem for infinity local systems, namely, the A∞-fuctor DR : InfLoc∞(g,M) → Loc∞(MG).eng
dc.description.curricularareaÁrea Curricular en Matemáticasspa
dc.description.degreelevelDoctoradospa
dc.description.degreenameDoctor en Ciencias - Matemáticasspa
dc.format.extent92 páginasspa
dc.format.mimetypeapplication/pdfspa
dc.identifier.instnameUniversidad Nacional de Colombiaspa
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombiaspa
dc.identifier.repourlhttps://repositorio.unal.edu.co/spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/83348
dc.language.isoengspa
dc.publisherUniversidad Nacional de Colombiaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellínspa
dc.publisher.facultyFacultad de Cienciasspa
dc.publisher.placeMedellín, Colombiaspa
dc.publisher.programMedellín - Ciencias - Doctorado en Ciencias - Matemáticasspa
dc.relation.indexedRedColspa
dc.relation.indexedLaReferenciaspa
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacionalspa
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/spa
dc.subject.ddc510 - Matemáticasspa
dc.subject.ddc510 - Matemáticas::516 - Geometríaspa
dc.subject.lembGeometría diferencial
dc.subject.lembGeometry, differential
dc.subject.proposalSistemas localesspa
dc.subject.proposalÁlgebra homotópicaspa
dc.subject.proposalHomomorfismo de Chern-Weilspa
dc.subject.proposalCohomología equivariantespa
dc.titleCategorification of Chern-Weil theory and equivariant cohomologyeng
dc.title.translatedCategorificación de la teoría de Chern-Weil y la cohomología equivariantespa
dc.typeTrabajo de grado - Doctoradospa
dc.type.coarhttp://purl.org/coar/resource_type/c_db06spa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/doctoralThesisspa
dc.type.redcolhttp://purl.org/redcol/resource_type/TDspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
dcterms.audience.professionaldevelopmentInvestigadoresspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa
oaire.fundernameColfuturospa

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