Domains of discontinuity for (quasi-)Hitchin representations
Prof.Daniele Alessandrini(Universität Heidelberg)
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
Among representations of surface groups into Lie groups, the Anosov representations are the ones with the nicest dynamical properties.
Guichard-Wienhard and Kapovich-Leeb-Porti have shown that their actions on generalized flag manifolds often admit co-compact domains of discontinuity, whose quotients are closed manifolds carrying interesting geometric structures.
Dumas and Sanders studied the topology and the geometry of the quotient in the case of quasi-Hitchin representations (Anosov representations which are deformations of Hitchin representations). In a conjecture they ask whether these manifolds are homeomorphic to fiber bundles over the surface.
In joint work with Qiongling Li, we can prove that the conjecture is true for (quasi-)Hitchin representations in SL(n,R) and SL(n,C), acting on projective spaces and partial flag manifolds parametrizing points and hyperplanes.