English

Hyperbolic extensions of free groups from atoroidal ping-pong

Group Theory 2019-05-29 v3 Geometric Topology

Abstract

We prove that all atoroidal automorphisms of Out(FN)Out(F_N) act on the space of projectivized geodesic currents with generalized north-south dynamics. As an application, we produce new examples of non virtually cyclic, free and purely atoroidal subgroups of Out(FN)Out(F_N) such that the corresponding free group extension is hyperbolic. Moreover, these subgroups are not necessarily convex cocompact.

Keywords

Cite

@article{arxiv.1711.07923,
  title  = {Hyperbolic extensions of free groups from atoroidal ping-pong},
  author = {Caglar Uyanik},
  journal= {arXiv preprint arXiv:1711.07923},
  year   = {2019}
}

Comments

v3: 17pp, 1 figure, minor corrections and clarifications following the referee's comments

R2 v1 2026-06-22T22:53:02.719Z