Contracting orbits in Outer space
Abstract
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 BestvinaFeighn, and is used to give conditions for when a subgroup of $\mathrm{Out}(\mathbb{F})$ has a quasiisometric orbit map into the free factor complex. It also allows one to construct many new examples of strongly contracting geodesics in Outer space.
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 arXiv:
 arXiv:1502.04053
 Bibcode:
 2015arXiv150204053D
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Group Theory
 EPrint:
 v3: 20 pages. minor corrections and changes based on referee comments. Final version