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

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    Genre
    Post-print
    Date
    2017-01-01
    Author
    Koberda, T
    Mangahas, J
    Taylor, SJ
    Subject
    Right-angled Artin group
    extension graph
    convex cocompact sub-group
    loxodromic isometry
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/4968
    
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    DOI
    10.1090/tran/6933
    Abstract
    © 2017 American Mathematical Society. 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.
    Citation to related work
    American Mathematical Society (AMS)
    Has part
    Transactions of the American Mathematical Society
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/4950
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