Simultaneous construction of hyperbolic isometries
arXiv:1609.05579 · doi:10.2140/pjm.2018.294.71
Abstract
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.
18 pages; v2: slight strengthening of main theorem, incorporated comments from referee, to appear in Pacific Journal of Mathematics