Strongly Contracting Geodesics in Outer Space
By Yael Algom-Kfir. 2008
84 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d23dd7f30e31ff299dfdb6baf07ac28bc2b3f80c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Denis V. Osin
- Vincent Guirardel
- Alessandro Sisto
- Franccois Dahmani
- M. Bestvina
- Dominik Gruber
- Anthony Genevois
- Goulnara Arzhantseva
In Mathematical Physics
- Denis V. Osin
- Vincent Guirardel
- Alessandro Sisto
- M. Bestvina
- Franccois Dahmani
- Dominik Gruber
- Goulnara Arzhantseva
- Ruth Charney
Citations in the corpus
- Characterizations of Morse Quasi-Geodesics via Superlinear Divergence and Sublinear Contraction (2016, background): “Pseudo-Anosov axes in Teichmüller space are strongly contracting [24], as are iwip axes in the Outer Space of the outer automorphism group of a free group [1] and axes of rank 1 isometries of CAT(0) spaces [4, 8].”
- METRIC PROPERTIES OF OUTER SPACE (2008, methodology): “Is there any analogue of the bounded projection Lemma? (see [5] and the recent preprint [1]).”
- Hyperbolicity of the complex of free factors (2011, methodology): “The first two hints that Outer space has some hyperbolic features was provided by Yael Algom-Kfir’s thesis [1] and by [5].”
- Contracting boundaries of CAT(0) spaces (2013, background): “The fact that (1) implies (2) is a well-known result, an explicit proof of which is given by Algom-Kfir [1].”
- Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “Examples of constricted groups include relatively hyperbolic groups [58], all but finitely many mapping class groups [18], Out(Fn) for n ≥ 2 [3], and many “exotic” groups such as Tarski Monsters [116].”
- Growth tight actions (2014, background): “Algom-Kfir [1] has proven an analogue of Minsky’s theorem that says that a fully irreducible outer automorphism class is strongly contracting for the action of Out(Fn) on its Outer Space, which is the analogue of the Teichmüller space.”