On Borel Anosov representations in even dimensions

Abstract

We prove that a word hyperbolic group which admits a $P_{2q+1}$-Anosov representation into $\mathsf{PGL}(4q+2,\mathbb{R})$ contains a finite-index subgroup which is either free or a surface group. As a consequence, we give an affirmative answer to Sambarino's question for Borel Anosov representations into $\mathsf{SL}(4q+2,\mathbb{R})$.