Atribución-NoComercial-SinDerivadas 4.0 InternacionalQuintero Vélez, AlexanderArias Abad, CamiloPineda Montoya, Santiago2023-02-072023-02-072022-06-28https://repositorio.unal.edu.co/handle/unal/83348diagramasEsta 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)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).92 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/510 - Matemáticas510 - Matemáticas::516 - GeometríaTrabajo de grado - DoctoradoUniversidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/info:eu-repo/semantics/openAccessGeometría diferencialGeometry, differentialSistemas localesÁlgebra homotópicaHomomorfismo de Chern-WeilCohomología equivariante