Cubulated hyperbolic groups admit Anosov representations

Abstract

We prove that any hyperbolic group acting properly discontinuously and cocompactly on a $\mathrm{CAT}(0)$ cube complex admits a projective Anosov representation into $\mathrm{SL}(d,\mathbb{R})$ for some $d$. More specifically, we show that if $\Gamma$ is a hyperbolic quasiconvex subgroup of a right-angled Coxeter group $C$, then a generic representation of $C$ by reflections restricts to a projective Anosov representation of $\Gamma$.

59 pages, 13 figures

References in corpus (4)

• Klein-Maskit combination theorem for Anosov subgroups: Free products
• On Borel Anosov subgroups of $\mathrm{SL}(d,\mathbb{R})$
• Morse actions of discrete groups on symmetric spaces: Local-to-global principle
• Special cubulation of strict hyperbolization