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arXiv · 1504.05172

On purely loxodromic actions

Ilya Kapovich
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Abstract

We construct an example of an isometric action of $F(a,b)$ on a $δ$-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 $F(a,b)\to Y$ is not a quasi-isometric embedding.

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Ilya Kapovich. 2015-07-07. On purely loxodromic actions. https://doi.org/10.1007/s00605-015-0795-7

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