### BULLETIN DES SCIENCES MATHEMATIQUES

#### Article

Let G be a real reductive Lie group, and H-C the complexification of its maximal compact subgroup H subset of G. We consider classes of semistable G-Higgs bundles over a Riemann surface X of genus g >= 2 whose underlying H-C-principal bundle is unstable. This allows us to find obstructions to a deformation retract from the moduli space of G-Higgs bundles over X to the moduli space of H-C-bundles over X, in contrast with the situation when g = 1, and to show reducibility of the nilpotent cone of the moduli space of G-Higgs bundles, for G complex.

C Florentino

A Nozad

### Publication

Year of publication: 2019

### Identifiers

ISSN: 0007-4497

Other: 2-s2.0-85058209813