English

Contracting orbits in Outer space

Geometric Topology 2018-12-05 v3 Group Theory

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 Bestvina--Feighn, and is used to give conditions for when a subgroup of Out(F)\mathrm{Out}(\mathbb{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.

Cite

@article{arxiv.1502.04053,
  title  = {Contracting orbits in Outer space},
  author = {Spencer Dowdall and Samuel J. Taylor},
  journal= {arXiv preprint arXiv:1502.04053},
  year   = {2018}
}

Comments

v3: 20 pages. minor corrections and changes based on referee comments. Final version; accepted for publication in MathZ

R2 v1 2026-06-22T08:29:14.034Z