Strongly contracting geodesics in Outer Space
Copyright policy )Strongly contracting geodesics in Outer Space
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.
37 pages. Revised applications chapter
- Yale University United States
Topological methods in group theory, 20E36, 20E05, Free nonabelian groups, Geometric Topology (math.GT), Group Theory (math.GR), outer space, automorphisms of free groups, Automorphisms of infinite groups, Mathematics - Geometric Topology, Asymptotic properties of groups, fully irreducible automorphisms, hyperbolic isometries, FOS: Mathematics, Thurston asymmetric metric, 20F65, pseudo-Anosov mapping classes, Teichmüller theory for Riemann surfaces, Geometric group theory, Mathematics - Group Theory
Topological methods in group theory, 20E36, 20E05, Free nonabelian groups, Geometric Topology (math.GT), Group Theory (math.GR), outer space, automorphisms of free groups, Automorphisms of infinite groups, Mathematics - Geometric Topology, Asymptotic properties of groups, fully irreducible automorphisms, hyperbolic isometries, FOS: Mathematics, Thurston asymmetric metric, 20F65, pseudo-Anosov mapping classes, Teichmüller theory for Riemann surfaces, Geometric group theory, Mathematics - Group Theory
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