Strongly Contracting Geodesics in Outer Space
Abstract
We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(Fn) 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(Fn) are stable, meaning that a quasi-geodesic with endpoints on the axis stays within a bounded distance from the axis.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.