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

2017/02/05 by Hung Cong Tran, Tran, Hung Cong
Mathematics · #Advanced Operator Algebra Research #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1702.01430

openalex publication_date 2017/02/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Let \Γ be a simplicial, finite, connected graph such that \Γ does\nnot decompose as a nontrivial join. We prove that two notions of strong\nquasiconvexity and stability are equivalent in the right-angled Artin group\nA_\Γ (except for the case of finite index subgroups). We also\ncharacterize non-trivial strongly quasiconvex subgroups of infinite index in\nA_\Γ (i.e. non-trivial stable subgroups in A_\Γ) by quadratic lower\nrelative divergence. These results strengthen the work of\nKoberda-Mangahas-Taylor on characterizing purely loxodromic subgroups of\nright-angled Artin groups.\n

Related

• Divergence and quasimorphisms of right-angled Artin groups
• The asymptotic geometry of right-angled Artin groups, I
• Stable subgroups of graph products
• When does a right-angled Artin group split over ℤ?
• Malnormality and join-free subgroups in right-angled Coxeter groups