Vol. 294, No. 1, 2018

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Simultaneous construction of hyperbolic isometries

Matt Clay and Caglar Uyanik

Vol. 294 (2018), No. 1, 71–88

Given isometric actions by a group G on finitely many δ-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.

hyperbolic isometries, free groups, fully irreducible
Mathematical Subject Classification 2010
Primary: 20F65
Received: 11 November 2016
Revised: 7 November 2017
Accepted: 14 November 2017
Published: 5 January 2018
Matt Clay
Department of Mathematical Sciences
University of Arkansas
Fayetteville, AR
United States
Caglar Uyanik
Department of Mathematics
Vanderbilt University
Nashville, TN
United States