Stability in Outer space

  • Ursula Hamenstädt

    Universität Bonn, Germany
  • Sebastian Hensel

    Universität Bonn, Germany


We characterize strongly Morse quasi-geodesics in Outer space as quasi-geodesics which project to quasi-geodesics in the free factor graph. We define convex cocompact subgroups of Out as subgroups such that an orbit map in the free factor graph is a quasi-isometric embedding, and we characterize such groups via their action on Outer space in a way which resembles the characterization of convex cocompact subgroups of mapping class groups.

Cite this article

Ursula Hamenstädt, Sebastian Hensel, Stability in Outer space. Groups Geom. Dyn. 12 (2018), no. 1, pp. 359–398

DOI 10.4171/GGD/445