André Oliveira
Centro de Matemática, Univ. Porto
Abstract: Let G be a real connected semisimple Lie group. The moduli spaces M(G) of G-Higgs bundles over a compact Riemann surface carry a very rich topological structure, which has been extensively studied in the last. decades. There is a. long story even for the most basic topological invariant - the number of connected components. For most groups G it is known that ∏0(M(G)) = ∏1(G), but there are some families of real Lie groups (split forms and groups of hermitian type) for which it is known that there are extra connected components. Until recently it was not known other kinds of groups for which M(G) has these exotic components. In this talk I will explain how we found that the indefinite special orthogonal group provides the first example of such a case.
This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.