Simultaneous construction of hyperbolic isometries

Matt Clay and Caglar Uyanik

Vol. 294 (2018), No. 1, 71–88

DOI: 10.2140/pjm.2018.294.71

Abstract

Given isometric actions by a group $G$ on finitely many $\delta$-hyperbolic metric spaces, we provide a sufficient condition that guarantees the existence of a single element in $G$ that is hyperbolic for each action. As an application we prove a conjecture of Handel and Mosher regarding relatively fully irreducible subgroups and elements in the outer automorphism group of a free group.

Keywords

hyperbolic isometries, free groups, fully irreducible

Mathematical Subject Classification 2010

Primary: 20F65

Milestones

Received: 11 November 2016

Revised: 7 November 2017

Accepted: 14 November 2017

Published: 5 January 2018