Representation Variety of Fuchsian Groups in SO(p,q)

TL;DR

This paper estimates the dimension of the variety of Zariski dense homomorphisms from Fuchsian groups to indefinite orthogonal groups, advancing understanding of their representation varieties.

Contribution

It provides a new estimate for the dimension of the variety of homomorphisms from Fuchsian groups into SO(p,q) with Zariski dense image.

Findings

Dimension estimates for the variety of homomorphisms

Characterization of Zariski dense representations

Insights into the structure of representation varieties

Abstract

We estimate the dimension of the variety of homomorphisms from $\Gamma$ to $ SO(p,q)$ with Zariski dense image, where $\Gamma$ is a Fuchsian group, and $SO(p,q)$ is the indefinite special orthogonal group with signature $(p,q)$.