Simple Anosov representations of closed surface groups

2023/07/06 by Nicolas Tholozan, Tholozan, Nicolas, Tianqi Wang +1
Mathematics · Computer Science · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2307.02934

Abstract

We introduce and study simple Anosov representations of closed hyperbolic surface groups, analogous to Minsky's primitive stable representations of free groups. We prove that the set of simple Anosov representations into SL(d,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.

Citations

• Dehn filling in relatively hyperbolic groups
• d‐Pleated surfaces and their shear‐bend coordinates

Related

• On boundary maps of Anosov representations of a surface group to SL(3,R)
• Topological restrictions on relatively Anosov representations
• Anosov deformations of Barbot representations
• Certifying Anosov representations
• On Borel Anosov representations in even dimensions