Matemática

URI Permanente desta comunidade

http://repositorio.ufes.br/handle/10/17495
Programa de Pós-Graduação em Matemática

Centro: CCE
Telefone: (27) 4009 2474
URL do programa: http://www.matematica.ufes.br/pos-graduacao/PPGMAT

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Navegando Matemática por Autor "Batoréo, Marta Jakubowicz"

Agora exibindo 1 - 3 de 3
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    Caracterização geométrica do espaço moduli de conexões ASD do fibrado de Hopf quatérnio
    (Universidade Federal do Espírito Santo, 2017-03-06) Maroja, Aaron Aragon; Câmara, Leonardo Meireles; Bursztyn, Henrique; Batoréo, Marta Jakubowicz
    In the early 80’s, C.C. Taubes and K. Uhlenbeck provided the analytical foundations so that the solutions of the Yang-Mills equations, called instantons, would have a geometrical use, yet to be found in the same period. Simon Donaldson has built then a theory based on certain aspects of these solutions over 4-dimensional, oriented, closed, differentiable manifolds. In this context, one can isolate a class of connections, called anti-self-dual, that necessarily sastify the Yang-Mills equation. The collection of all such, modulo a natural equivalence relation, namely gauge equivalence, is called the moduli space M of the bundle and its study has led to astonishing insights into the structure of smooth 4- manifolds. This work is set to study in detail a particular example of Donaldson’s Theory on the Hopf bundle over the 4-dimensional manifold ?? 4 . We arrive at the BPST instantons of such bundle via the Cartan canonical 1-form on ????(2). Once these are in hand, we use the conformal invariance of anti-self-dual equations to write down a 5-parameter family of such connections. By making use of a theorem of Atiyah, Hitchin and Singer, we assert that every element of the moduli space M is uniquely represented by a connection in this family. From this we obtain a concrete realization of M as the open unit ball in R 5 . In particular, M is a 5-dimensional manifold with a natural compactification whose boundary is a copy of the base space ?? 4 .
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    Homologia de Morse e uma aplicação em geometria simplética
    (Universidade Federal do Espírito Santo, 2023-05-29) Flores, Thales Danton de Souza; Batoréo, Marta Jakubowicz; http://lattes.cnpq.br/1461528961848898; http://lattes.cnpq.br/0978245375441146; Nascimento, José Victor Goulart; https://orcid.org/0000-0001-6660-792X; http://lattes.cnpq.br/5273512936573286; Balseiro, Paula; http://lattes.cnpq.br/7655880123530492
    In this work some concepts and main results of Morse theory are presented, such as Morse’s lemma and Smale’s theorem. Furthermore, we will present a particular case of Arnold’s conjecture which is an application of Morse theory in symplectic geometry.
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    O Teorema da Separação de Jordan-Brouwer em variedades diferenciáveis
    (Universidade Federal do Espírito Santo, 2019-05-06) Giovanelli, Joelso; Batoréo, Marta Jakubowicz; Desideri, Patricia Elaine; Câmara, Leonardo Meireles; Mandini, Alessia
    This dissertation presents a proof of the Jordan-Brouwer Theorem. This theorem states, roughly, that a hypersurface of the euclidean space R n divides the space in two sets: the “inside”and the “outside”. The proof relies on techniques from Differential Topology, e.g., transversality and winding numbers. The main reference for this work is [GP74].