Strongly contracting geodesics in Outer Space

Algom-Kfir, Yael

doi:10.2140/gt.2011.15.2181

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Strongly contracting geodesics in Outer Space

Yael Algom-Kfir

Geometry & Topology 15 (2011) 2181–2233

DOI: 10.2140/gt.2011.15.2181

Abstract

We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of $Out (F_{n})$ 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 $Out (F_{n})$ 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

Volume 15, issue 4 (2011)