Strong quasiconvexity, stability, and lower relative divergence in right-angled Artin groups

Abstract

Let $\Gamma$ be a simplicial, finite, connected graph such that $\Gamma$ does not decompose as a nontrivial join. We prove that two notions of strong quasiconvexity and stability are equivalent in the right-angled Artin group $A_{\Gamma }$ (except for the case of finite index subgroups). We also characterize non-trivial strongly quasiconvex subgroups of infinite index in $A_{\Gamma }$ (i.e. non-trivial stable subgroups in $A_{\Gamma }$) by quadratic lower relative divergence. These results strengthen the work of Koberda-Mangahas-Taylor on characterizing purely loxodromic subgroups of right-angled Artin groups.

This article has been subsumed by the preprint arXiv:1707.05581

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