Abstract: In this talk, I aim to give an overview of some known results and several open questions concerning geometric and topological properties of the moduli space Mk,d of stable Higgs bundles (of rank k and degree d) on a compact Riemann surface ∑. I shall in particular discuss the construction of Mk,d as the space of gauge equivalence classes of solutions to Hitchin’s selfduality equations. Some recent results (obtained jointly with Rafe Mazzeo, Hartmut Weiß and Frederik Witt) concerning the structure of ends of M2,d as well as the large scale geometry of a naturally defined hyperkähler metric will be presented. If time permits, I will also discuss a gluing construction which allows to compare M2,d with its counterpart comprising singular solutions on a noded Riemann surface.
Geometric and analytic aspects of Higgs bundle moduli spaces (GGT-Seminar)
SR 1.067 (20.30)
Dr. Jan Swoboda