The geometry of quasi-Hitchin symplectic Anosov representations

Geometry & Topology
Event time: 
Tuesday, November 17, 2020 - 4:00pm
Sara Maloni
Speaker affiliation: 
University of Virginia
Event description: 

In this talk we will discuss quasi-Hitchin representations in Sp(4,C). In the same way that Hitchin representations correspond to a natural higher-rank generalization of Fuchsian representations, quasi-Hitchin representations correspond to a higher-rank generalization of quasi-Fuchsian representations. Unfortunately, in the higher rank setting, an interpretation in term of geometric structures is much less obvious than in the classical case, and this is what we will discuss in this talk in the specific case of quasi-Hitchin representations in Sp(4,C). Our result will follow from a parametrization of the space Lag(C^4) of complex lagrangian grassmanian subspaces of C^4 as the space of regular ideal hyperbolic tetrahedra and their degenerations. This theory generalizes the classical and important theory of quasi-Fuchsian representations and their action on the Riemann sphere CP^1 = Lag (C^2). (This is joint work with D. Alessandrini and A. Wienhard.)

Special note: 
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