Anosov groups that are indiscrete in rank one

Abstract

We exhibit Anosov subgroups of ${\mathsf{SL}}_d(\mathbb{R})$ that do not embed discretely in any rank-$1$ simple Lie group of noncompact type, or indeed, in any finite product of such Lie groups. These subgroups are isomorphic to free products $\Gamma \ast \Delta$, where $\Gamma$ is a uniform lattice in ${\mathsf{F}}_4^{(-20)}$ and $\Delta$ is a uniform lattice in $\mathsf{Sp}(m,1)$, $m\ge 51$.

arXiv commentFinal version. Published in IMRN