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Divergence of CP^1-structures on surfaces and convergence in PSL(2, C)-character varieties

Shinpei Baba (Universität Heidelberg)
Torsdag, 19 maj, 2016, at 15:15-16:15, in Aud. D3 (1531-215)
A CP^1-structure on a surface is a certain locally homogeneous structure, and it can be regarded as a pair of a Riemann surface and a holomorphic quadratic differential (on it). A CP^1-structure also corresponds to a representation of the fundament group of the surface into PSL(2, C).

In this talk, we consider a one-parameter family of diverging CP^1-structures on a closed surface of genus at least two, and we describe its limit under the assumption that the family of their representations converges in the PSL(2, C)-character variety and that the family of their Riemann surface structures is asymptotically pinched along disjoint loops (in a coarse sense).
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen