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

Daniele Alessandrini (University of Heidelberg)
Onsdag, 21 september, 2016, at 16:15-17:15, in Aud. D3 (1531-215)
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.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen