For uniform lattices $\Gamma$ in rank 1 Lie groups, we construct Anosov representations of virtual doubles of $\Gamma$ along certain quasiconvex subgroups. We also show that virtual HNN extensions of these lattices over some cyclic subgroups admit Anosov embeddings. In addition, we prove that for any Anosov subgroup $\Gamma$ of a real semisimple linear Lie group $\mathsf{ G}$ and any infinite abelian subgroup $\mathrm{ H} $ of $ \Gamma$, there exists a finite-index subgroup $\Gamma' $ of $ \Gamma$ containing $\mathrm{ H}$ such that the double $\Gamma' *_{ \mathrm{ H}} \Gamma'$ admits an Anosov representation, thereby confirming a conjecture of [arXiv:2112.05574]. These results yield numerous examples of one-ended hyperbolic groups that do not admit discrete and faithful representations into rank 1 Lie groups but do admit Anosov embeddings into higher-rank Lie groups.
Categories: math.GR math.DS math.GT