| Résume | 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). |
