Autonomous University of Madrid. Madrid (Spain)
July 26th, 2018
Summary:
This thesis is concerned with the study of some augmented bundles equipped with real structures. More specifically, we study: real Higgs pairs, real G-Higgs bundles and real parabolic G-Higgs bundles, where G is a real form of a connected semisimple group G^C. These bundles generalize the notion of pseudo-real Higgs bundles. We prove that they appear naturally as fixed points of involutions in the moduli space of Higgs pairs, G-Higgs bundles and parabolic G-Higgs bundles, respectively. We also prove a non-abelian Hodge correspondence for real G-Higgs bundles and real parabolic G-Higgs bundles.
The motivation is given by the study of fixed points in the moduli space of augmented bundles and the fact that these fixed points are branes in the sense of Kapustin-Witten in the theory of Geometry Langlands program. Another future research line will be the Higher Teichmuller theory in the presence of real structures.
Descriptors: Differential geometry
Keywords: Real Higgs bundles; Parabolic Higgs bundles; Real structures; Moduli spaces; Non-abelian Hodge correspondence; Branes; Geometric Langlands program; Real forms of semisimple groups; Higher Teichmüller theory.
Citation:
L.A. Calvo, "Augmented bundles and real structures", PhD. dissertation, Autonomous University of Madrid, Madrid, Spain, 2018.
