Domains of discontinuity for Anosov representations

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 Teichmüller Spaces, spaces that generalize the classical Teichmüller 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.