Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, E. Di Nezza, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, eleonora.dinezza, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

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Orateur(s) Oscar Garcia Prada - ICMAT, Madrid,
Titre Cyclic Higgs bundles and the Toledo invariant
Horaire14:00 à 15:00

Given a compact Riemann surface X and a semisimple complex Lie group G, we consider the moduli space M(X,G) of G-Higgs bundles over X. Cyclic Higgs bundles are fixed points in M(X,G) under the action of a finite cyclic group. These are described in terms of Vinberg pairs defined by a Z/mZ-grading of the Lie algebra of G. When m=2 the fixed points are in bijection, under the non-abelian Hodge correspondence, with representations of the fundamental group of X into real forms of G. Based on recent joint work with Biquard, Collier and Toledo, in this talk I will describe a generalization of the Toledo invariant and Milnor-Wood type inequality for a certain class of cyclic Higgs bundles (joint work with Miguel Gonzalez).