Strongly contracting geodesics in Outer Space

Algom-Kfir, Yael¹

¹ Department of Mathematics, Yale University, PO Box 208283, New Haven CT 06511, USA

Geometry & topology, Tome 15 (2011) no. 4, pp. 2181-2233.

Résumé

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.

Détail

DOI : 10.2140/gt.2011.15.2181

Classification : 20E05, 20E36, 20F65

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