Representation varieties of Fuchsian groups

Abstract

We estimate the dimension of varieties of the form Hom(F,G) where F is a Fuchsian group and G is a simple real algebraic group, answering along the way a question of I. Dolgachev.

Lemma 2.3 of version 1 (renumbered 3.3 in this version for consistency with the published version) was incorrect as stated. This version proves a weaker version of Lemma 3.3 and a correspondingly strengthened version of Theorem 3.4. The main theorems are unchanged