# Contracting orbits in Outer space

@article{Dowdall2019ContractingOI, title={Contracting orbits in Outer space}, author={Spencer Dowdall and Samuel J. Taylor}, journal={Mathematische Zeitschrift}, year={2019}, volume={293}, pages={767-787} }

We show that strongly contracting geodesics in Outer space project to parameterized quasigeodesics in the free factor complex. This result provides a converse to a theorem of Bestvina–Feighn, and is used to give conditions for when a subgroup of $${{\,\mathrm{Out}\,}}(\mathbb {F})$$Out(F) has a quasi-isometric orbit map into the free factor complex. It also allows one to construct many new examples of strongly contracting geodesics in Outer space.

## 3 Citations

### Pulling back stability with applications to Out(Fn) and relatively hyperbolic groups

- MathematicsJ. Lond. Math. Soc.
- 2017

It is proved that stability – a strong quasiconvexity property – pulls back under proper actions on proper metric spaces, including that convex cocompact subgroups of both mapping class groups and outer automorphism groups of free groups are stable.

### Random walks and quasi‐convexity in acylindrically hyperbolic groups

- MathematicsJournal of Topology
- 2021

Arzhantseva proved that every infinite‐index quasi‐convex subgroup H of a torsion‐free hyperbolic group G is a free factor in a larger quasi‐convex subgroup of G . We give a probabilistic…

### Counting conjugacy classes of fully irreducibles: double exponential growth

- Mathematics
- 2018

Inspired by results of Eskin and Mirzakhani~\cite{EM11} counting closed geodesics of length $\le L$ in the moduli space of a closed surface $\Sigma_g$ of genus $g\ge 2$, we consider a similar…

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