The geometry of purely loxodromic subgroups of right-angled Artin groups

2014/12/11 by Thomas Koberda, Koberda, Thomas, Johanna Mangahas +3 · 3 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1412.3663

39 pages, 10 figures. To appear in Transactions of the AMS

arxiv created 2016/03/08 · arxiv updated 2016/03/10

Abstract

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group A(Γ) fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups Mod(S). In particular, such subgroups are quasiconvex in A(Γ). In addition, we identify a milder condition for a finitely generated subgroup of A(Γ) that guarantees it is free, undistorted, and retains finite generation when intersected with A(Λ) for subgraphs Λ of Γ. These results have applications to both the study of convex cocompactness in Mod(S) and the way in which certain groups can embed in right-angled Artin groups.

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