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On purely loxodromic actions

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Abstract

We construct an example of an isometric action of F(a, b) on a \(\delta \)-hyperbolic graph Y, such that this action is acylindrical, purely loxodromic, has asymptotic translation lengths of nontrivial elements of F(a, b) separated away from 0, has quasiconvex orbits in Y, but such that the orbit map \(F(a,b)\rightarrow Y\) is not a quasi-isometric embedding.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL, 61801, USA

    Ilya Kapovich

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  1. Ilya Kapovich
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Correspondence to Ilya Kapovich.

Additional information

Communicated by J. S. Wilson.

The author was partially supported by the NSF Grant DMS-1405146.

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Kapovich, I. On purely loxodromic actions. Monatsh Math 181, 89–101 (2016). https://doi.org/10.1007/s00605-015-0795-7

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  • DOI: https://doi.org/10.1007/s00605-015-0795-7

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