#### Volume 15, issue 4 (2011)

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Strongly contracting geodesics in Outer Space

### Yael Algom-Kfir

Geometry & Topology 15 (2011) 2181–2233
##### Abstract

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of $Out\left({F}_{n}\right)$ act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of $Out\left({F}_{n}\right)$ are Morse, meaning that a quasi-geodesic with endpoints on the axis stays within a bounded distance from the axis.

##### Mathematical Subject Classification 2010
Primary: 20E05
Secondary: 20E36, 20F65
##### Publication
Received: 18 May 2010
Revised: 10 June 2011
Accepted: 26 August 2011
Published: 11 November 2011
Proposed: Benson Farb
Seconded: Walter Neumann, Martin Bridson
##### Authors
 Yael Algom-Kfir Department of Mathematics Yale University PO Box 208283 New Haven CT 06511 USA