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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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(Fn) 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(Fn) 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
References
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