Repositório Colecção:
http://hdl.handle.net/10348/3945
2023-06-03T15:35:21ZPrincipal bundles on 2-dimensional CW-complexes with disconnected structure group
http://hdl.handle.net/10348/10843
Título: Principal bundles on 2-dimensional CW-complexes with disconnected structure group; Principal bundles on 2-dimensional CW-complexes with disconnected structure group
Autor: Oliveira, Andre Gama; Oliveira, Andre Gama
Resumo: Given any topological group G, the topological classification of principal G-bundles over a finite CW-complex X is long-known to be given by the set of free homotopy classes of maps from X to the corresponding classifying space BG. This classical result has been long-used to provide such classification in terms of explicit characteristic classes. However, even when X has dimension 2, it seems there is a case in which such explicit classification has not been explicitly considered. This is the case where G is a Lie group, whose group of components acts non-trivially on its fundamental group π1G. In this note we deal with this case by obtaining the classification, in terms of characteristic classes, of principal G-bundles over a finite CW-complex of dimension 2, with G is a Lie group such that π0G is abelian.2021-01-01T00:00:00ZUnramified covers and branes on the Hitchin system
http://hdl.handle.net/10348/10309
Título: Unramified covers and branes on the Hitchin system
Autor: Franco, Emilio; Gothen, Peter; Oliveira, Andre Gama; Peon-Nieto, Ana
Resumo: We study the locus of the moduli space of GL(n,C)-Higgs bundles on a curve givenby those Higgs bundles obtained by pushforward under a connected unramified cover. We equipthese loci with a hyperholomorphic bundle so that they can beviewed as BBB-branes, and weintroduce corresponding BAA-branes which can be describedvia Hecke modifications. Wethen show how these branes are naturally dual via explicit Fourier–Mukai transform (recall that GL(n,C) is Langlands self dual). It is noteworthy that these branes lie over the singularlocus of the Hitchin fibration.As a particular case, our construction describes the behavior under mirror symmetry of thefixed loci for the action of tensorization by a line bundle of ordern. These loci play a key rolein the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces.2020-11-01T00:00:00ZComplex Lagrangians in a hyperKaehler manifold and the relative Albanese
http://hdl.handle.net/10348/10215
Título: Complex Lagrangians in a hyperKaehler manifold and the relative Albanese
Autor: Biswas, Indranil; Gómez, Tomas; Oliveira, Andre Gama
Resumo: Let M be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold X, and let A→ M be the relative Albanese over M. We prove that A has a natural holomorphic symplectic structure. The projection onto M deﬁnes a completely integrable structure on the symplectic manifold A. In particular, the ﬁbers are complex Lagrangians with respect to the symplectic form on A. We also prove analogous results for the relative Picard over M.2020-01-01T00:00:00ZSO(p,q)-Higgs bundles and Higher Teichmüller components
http://hdl.handle.net/10348/9478
Título: SO(p,q)-Higgs bundles and Higher Teichmüller components
Autor: Aparicio-Arroyo, Marta; Bradlow, Steven; Collier, Brian; García-Prada, Oscar; Gothen, Peter B.; Oliveira, André2019-01-01T00:00:00Z