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Seminar by Daniele Alessandrini (Heidelberg)

Title: The PSL(2,C) geometry of the Lagrangian Grassmannian

2016.08.08 | Jane Jamshidi

Date Wed 21 Sep
Time 16:15 17:15
Location 1531-215 (Aud. D3)

Quasi-Fuchsian representations of surface groups in PSL(2,C) are very important in Teichmüller theory. Their limit set in CP^1 is a circle, and the complement is a cocompact domain of discontinuity whose quotient is the union of two copies of the surface.

We want to understand how these properties generalize to higher rank lie groups. Quasi-Hitchin representations in Sp(4,C) are considered the analog of Quasi-Fuchsian representations. I will describe the action of these representations on the Lagrangian Grassmannian of C^4, where Guichard
and Wienhard proved they have a cocompact domain of discontinuity. The quotient of this domain by the action of the representation is a 6-manifold, and I will describe its topology. This is joint work with Sara Maloni and Anna Wienhard.