Strongly Contracting Geodesics in Outer Space

Details Strongly Contracting Geodesics in Outer Space Strongly Contracting Geodesics in Outer Space

2008-12-08

arxiv.org/abs/0812.1555v3

Mathematics

Group Theory

37 pages. Revised applications chapter

Scientific paper

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 stable, meaning that a quasi-geodesic with endpoints on the axis stays within a bounded distance from the axis.

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