Steven Bradlow - Exotic components of surface group representation varieties
Channel: UMD Mathematics
Date: 2017-09-11

Steven Bradlow
Exotic components of surface group representation varieties, and their Higgs bundle avatars

Moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. For representations into complex semisimple Lie groups, the components of these spaces are labeled by obvious topological invariants. This is no longer true if one restricts to real forms of the complex groups. Factors other than the obvious invariants lead to the existence of extra `exotic' components which can have special significance. Formerly, all known instances of such exotic components were attributable to one of two distinct mechanisms. Recent Higgs bundle results for the groups SO(p,q) shed new light on this dichotomy and reveal new examples outside the scope of the two known mechanisms. This talk will survey what is known about the exotic components and describe the new SO(p,q) results.