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