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Title:
Higgs bundles and exotic components of surface group representation varieties
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Abstract:
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. In contrast, for representations into real forms of the complex groups, features other than the obvious invariants lead to the existence of extra `exotic' components which can have special significance. Instances of such exotic components occur in so-called ``higher Teichmuller'' theory, where they have been attributed to one of two distinct mechanisms. We will describe results for SO(p,q)-Higgs bundle which reveal new examples outside the scope of these two mechanisms, and which provide evidence for a unifying explanation conjectured by Guichard-Labourie-Wienhard.
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