Domains of discontinuity for Anosov representations

Daniele Alessandrini (Columbia)

Abstract: The parameter spaces of Anosov representations can usually be seen as deformation spaces of parabolic geometric structures on some closed manifolds, this is due to Guichard-Wienhard and Kapovich-Leeb-Porti. A particularly interesting case is given by the Higher Teichmuller Spaces, spaces that generalize the classical Teichmuller spaces for higher rank Lie groups. In this talk we will present a general structure theorem about the topology of such closed manifolds, and we will describe this topology explicitly in some interesting cases. This is based on a joint work with Colin Davalo and Qiongling Li, and a joint work with Sara Maloni, Nicolas Tholozan and Anna Wienhard.