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Anosov groups that are indiscrete in rank one
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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 $\Gamma * \Delta$, where $\Gamma$ is a uniform lattice in $\mathsf{F}_4^{(-20)}$ and $\Delta$ is a uniform lattice in $\mathsf{Sp}(m,1)$, $m \geq 51$.
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Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio
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