|Tuesday 25 June 2019|
|Events for day: Wednesday 02 January 2019|
| 15:30 - 17:00 Geometry and Topology Weekly Seminar|
The Moduli Spaces of $G$-Higgs Bundles and the Nilpotent Cone
For a non-compact reductive Lie group $G$, the notion of $G$-Higgs bundles over a compact Riemann surface $X$, of genus $g geq2$, was introduced by Hitchin (80s and 90s). These are appropriate objects for extending the non-abelian Hodge Theorem (the work of Corlette, Donaldson, Hitchin and Simpson) to representations of the fundamental group in a real reductive Lie group $G$. Motivated partially by this identification, the moduli space of $G$-Higgs bundles has been extensively studied. Here we give the obstructions to a deformation retraction from the moduli spaces of $G$-Higgs bundles to the moduli space of semistable principal bundles over ...