Fenchel-Nielsen coordinates for SL(3,C) representations of surface groups

Teichmueller space can be viewed as the space of conjugacy classes of representations of a surface group into the isometry group of the hyperbolic plane. In the late 1940s Fenchel and Nielsen gave a set of geometrical coordinates for Teichmueller space. These have been generalised to quasi-Fuchsian groups, convex real projective structures and complex hyperbolic isometries. In this talk I will show how to generalise Fenchel-Nielsen coordinates to SL(3,C) representations and demonstrate how this unifies the original coordinates and their generalisations. It is joint work with Rodrigo Davila.

Bio
https://www.durham.ac.uk/staff/j-r-parker/