Categorification of Chern-Weil theory and equivariant cohomology
dc.contributor.advisor | Quintero Vélez, Alexander | |
dc.contributor.advisor | Arias Abad, Camilo | |
dc.contributor.author | Pineda Montoya, Santiago | |
dc.contributor.orcid | Arias Abad, Camilo [0000-0003-3624-9396] | spa |
dc.date.accessioned | 2023-02-07T14:02:58Z | |
dc.date.available | 2023-02-07T14:02:58Z | |
dc.date.issued | 2022-06-28 | |
dc.description | diagramas | spa |
dc.description.abstract | Esta 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.abstract | Let 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.curriculararea | Área Curricular en Matemáticas | spa |
dc.description.degreelevel | Doctorado | spa |
dc.description.degreename | Doctor en Ciencias - Matemáticas | spa |
dc.format.extent | 92 páginas | spa |
dc.format.mimetype | application/pdf | spa |
dc.identifier.instname | Universidad Nacional de Colombia | spa |
dc.identifier.reponame | Repositorio Institucional Universidad Nacional de Colombia | spa |
dc.identifier.repourl | https://repositorio.unal.edu.co/ | spa |
dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/83348 | |
dc.language.iso | eng | spa |
dc.publisher | Universidad Nacional de Colombia | spa |
dc.publisher.branch | Universidad Nacional de Colombia - Sede Medellín | spa |
dc.publisher.faculty | Facultad de Ciencias | spa |
dc.publisher.place | Medellín, Colombia | spa |
dc.publisher.program | Medellín - Ciencias - Doctorado en Ciencias - Matemáticas | spa |
dc.relation.indexed | RedCol | spa |
dc.relation.indexed | LaReferencia | spa |
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dc.rights.accessrights | info:eu-repo/semantics/openAccess | spa |
dc.rights.license | Atribución-NoComercial-SinDerivadas 4.0 Internacional | spa |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | spa |
dc.subject.ddc | 510 - Matemáticas | spa |
dc.subject.ddc | 510 - Matemáticas::516 - Geometría | spa |
dc.subject.lemb | Geometría diferencial | |
dc.subject.lemb | Geometry, differential | |
dc.subject.proposal | Sistemas locales | spa |
dc.subject.proposal | Álgebra homotópica | spa |
dc.subject.proposal | Homomorfismo de Chern-Weil | spa |
dc.subject.proposal | Cohomología equivariante | spa |
dc.title | Categorification of Chern-Weil theory and equivariant cohomology | eng |
dc.title.translated | Categorificación de la teoría de Chern-Weil y la cohomología equivariante | spa |
dc.type | Trabajo de grado - Doctorado | spa |
dc.type.coar | http://purl.org/coar/resource_type/c_db06 | spa |
dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa | spa |
dc.type.content | Text | spa |
dc.type.driver | info:eu-repo/semantics/doctoralThesis | spa |
dc.type.redcol | http://purl.org/redcol/resource_type/TD | spa |
dc.type.version | info:eu-repo/semantics/acceptedVersion | spa |
dcterms.audience.professionaldevelopment | Investigadores | spa |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 | spa |
oaire.fundername | Colfuturo | spa |
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