Volume of maximal representations into $\mathrm{SO}_0(2,3)$

TL;DR

This paper investigates the volume of maximal representations of surface groups into SO_0(2,3), establishing uniform upper bounds and positive lower bounds on specific components.

Contribution

It provides new bounds on the volume of maximal representations into SO_0(2,3), highlighting uniformity across surface genus and positivity in Gothen components.

Findings

Volume is bounded above uniformly in genus.

On Gothen components, volume is bounded below by a positive constant.

Results contribute to understanding geometric structures of surface group representations.

Abstract

We study the volume of maximal representations from a surface group into $\mathrm{SO}_0(2,3)$. We show that it is bounded from above, uniformly in the genus of the surface. We also prove that on the Gothen components, it is bounded from below by a strictly positive constant.