# 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}
}
• Published 13 February 2015
• Physics, Mathematics
• Mathematische Zeitschrift
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

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