Fenchel-Nielsen Coordinates for Maximal Representations
Differential Geometry
2012-04-04 v1 Group Theory
Abstract
We develop Fenchel-Nielsen coordinates for representations of surface groups into Sp(2n,R) with maximal Toledo invariant. Analogous to classical Fenchel-Nielsen coordinates on the Teichm\"uller space they consist of a parametrization of representations of the fundamental group of a pair of pants and a careful investigation of the gluing. As applications we obtain results for non-closed surfaces, which have been known only for closed surfaces before: we count the number of connected components of their representation space and prove continuity for the limit curve for a certain type of representations.
Cite
@article{arxiv.1204.0719,
title = {Fenchel-Nielsen Coordinates for Maximal Representations},
author = {Tobias Strubel},
journal= {arXiv preprint arXiv:1204.0719},
year = {2012}
}