Simple Anosov representations of closed surface groups

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 $d⩾4$ 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.

References in corpus (3)

• Dynamics on the PSL(2,C)-character variety of a twisted I-bundle
• Relatively Anosov representations via flows I: theory
• Relatively Anosov representations via flows II: examples