Topic
Out(Fn)
About: Out(Fn) is a research topic. Over the lifetime, 28 publications have been published within this topic receiving 630 citations.
Papers
TL;DR: In this paper, a bordification of outer space analogous to Borel-Serre bordifications of symmetric spaces is presented. But it is shown that Out(Fn) is (2n-5)-connected at infinity and that it is a virtual duality group of dimension 2n-3.
Abstract: We construct a bordification of Outer Space analogous to the Borel-Serre bordification of symmetric spaces. As an application, we show that Out(Fn) is (2n-5)-connected at infinity and that it is a virtual duality group of dimension 2n-3.
83 citations
TL;DR: For any finite collection of fully irreducible automorphisms of the free group Fn, this article constructed a connected i-hyperbolic Out in which each automorphism has positive translation length.
Abstract: For any finite collection fi of fully irreducible automorphisms of the free group Fn we construct a connected i-hyperbolic Out.Fn/-complex in which each fi has positive translation length.
70 citations
TL;DR: In this paper, the authors find dynamic invariants that completely determine elements of the outer automorphism group of the free group of rank n. This is not a serious restriction, since rotationless elements are represented by particularly nice relative train track maps.
Abstract: Our goal is to find dynamic invariants that completely determine elements of the outer automorphism group $\\Out(F_n)$ of the free group $F_n$ of rank $n$. To avoid finite order phenomena, we do this for {\\it forward rotationless} elements. This is not a serious restriction. For example, there is $K_n>0$ depending only on $n$ such that, for all $\\phi\\in\\Out(F_n)$, $\\phi^{K_n}$ is forward rotationless. An important part of our analysis is to show that rotationless elements are represented by particularly nice relative train track maps.
69 citations
TL;DR: In this paper, it was shown that if φ, ψ ∈ Out(FN) are hyperbolic iwips with irreducible powers, such that φ and ψ are not virtually cyclic, then a free subgroup of rank two can be generated for which all nontrivial elements are again Hyperbolic Iwips.
Abstract: We prove that, if φ, ψ ∈ Out(FN) are hyperbolic iwips (irreducible with irreducible powers) such that 〈φ, ψ〉 ⊆ Out(FN) is not virtually cyclic, then some high powers of φ and ψ generate a free subgroup of rank two for which all nontrivial elements are again hyperbolic iwips. Being a hyperbolic iwip element of Out(FN) is strongly analogous to being a pseudo-Anosov element of a mapping class group, so the above result provides analogues of "purely pseudo-Anosov" free subgroups in Out(FN).
49 citations
TL;DR: In this paper, an open set of PSL2(ℂ) characters of a nonabelian free group is studied, on which the action of the outer automorphism group is properly discontinuous, and which is strictly larger than the set of discrete, faithful convex-cocompact characters.
Abstract: We introduce and study an open set of PSL2(ℂ) characters of a nonabelian free group, on which the action of the outer automorphism group is properly discontinuous, and which is strictly larger than the set of discrete, faithful convex-cocompact (i.e. Schottky) characters. This implies, in particular, that the outer automorphism group does not act ergodically on the set of characters with dense image. Hence there is a difference between the geometric (discrete vs. dense) decomposition of the characters, and a natural dynamical decomposition.
42 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2019 | 1 |
| 2018 | 1 |
| 2017 | 1 |
| 2015 | 1 |
| 2014 | 1 |