On purely loxodromic actions

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 $F(a,b)\to Y$ is not a quasi-isometric embedding.

several minor fixes and updates; 9 pages, no figures; to appear in Monatshefte für Mathematik

References in corpus (2)

• Hyperbolic extensions of free groups
• The co-surface graph and the geometry of hyperbolic free group extensions

Cited by in corpus (2)

• Hyperbolic structures on groups
• The co-surface graph and the geometry of hyperbolic free group extensions