Seminar by Shinpei Baba (Univ. Heidelberg)

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

2016.05.09 | Jane Jamshidi

 Date Thu 19 May Time 15:15 — 16:15 Location 1530-215 (Aud. D3)

Abstract:

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).