Klein-Maskit combination theorem for Anosov subgroups: Free products

Abstract

We prove a generalization of the classical Klein-Maskit combination theorem, in the free product case, in the setting of Anosov subgroups. Namely, if ${\Gamma }_A$ and ${\Gamma }_B$ are Anosov subgroups of a semisimple Lie group $G$ of noncompact type, then under suitable topological assumptions, the group generated by ${\Gamma }_A$ and ${\Gamma }_B$ in $G$ is again Anosov, and is naturally isomorphic to the free product ${\Gamma }_A\ast {\Gamma }_B$. Such a generalization was conjectured in our previous article with Bernhard Leeb (arXiv:1805.07374).

arXiv commentFinal version after referee's comments, 26 pages. Accepted in Math. Z

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• On Borel Anosov subgroups of $\mathrm{SL}(d,\mathbb{R})$
• Morse actions of discrete groups on symmetric spaces: Local-to-global principle
• Cubulated hyperbolic groups admit Anosov representations