Given a closed, connected, oriented surface S of genus at least two, the SL(2,C) character variety is the space of conjugacy classes of reductive homomorphisms of the fundamental group of S into SL(2,C). In this talk, I will try to give a historical account of the (symplectic) geometry of this space, with the starting point being the discovery of Atiyah-Bott (and later Goldman) that the SL(2,C) character variety has a natural holomorphic symplectic structure. In the course of this discussion, we will meet Teichmuller space, quasi-Fuchsian space, and the space of complex projective structures on the surface S. The ultimate goal of this talk is to explain the remarkable interaction between geometrically defined coordinate systems on these spaces, and the behavior of the Atiyah-Bott-Goldman symplectic structure with respect to these coordinate systems.
Mittwoch, den 20. Juni 2018 um 16.00-18.00 Uhr Uhr, in Mathematikon, INF 205, SR 4 Mittwoch, den 20. Juni 2018 at 16.00-18.00 Uhr, in Mathematikon, INF 205, SR 4
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Benedetti