Simple Anosov representations of closed surface groups

TL;DR

This paper introduces simple Anosov representations for surface groups, expanding the class of known representations, and constructs new domains of discontinuity for the mapping class group action on character varieties.

Contribution

It defines simple Anosov representations for surface groups, showing they include more representations than classical Anosov ones, and constructs new domains of discontinuity.

Findings

Simple Anosov representations form a larger set than classical Anosov representations.

Constructed domains of discontinuity for the mapping class group action.

These domains include non-discrete representations.

Abstract

We introduce and study \emph{simple Anosov representations} of closed hyperbolic surface groups, analogous to Minsky's \emph{primitive stable representations} of free groups. We prove that the set of simple Anosov representations into $\mathrm{SL}(d,\mathbb{C})$ with $d \geqslant 4$ strictly contains the set of Anosov representations. As a consequence, we construct domains of discontinuity for the mapping class group action on character varieties which contain non-discrete representations.