A hyperbolic Out(Fn)-complex

By M. Bestvina, Mark Feighn. 2010

57 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b6d3da831c478ffcb3774c9dcb1296e77a0fc97c

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Citations in the corpus

Acylindrically hyperbolic groups (2013, background): “Bestvina and Feighn [6] proved that for every fully irreducible automorphism f ∈ Out ( F n ) there exists a hyperbolic graph such that Out ( F n ) acts on it and the action of f satisﬁes the weak proper discontinuity condition.”
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].”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “Recall that given Fn, and a finite family I of iwip elements in Out(Fn), Bestvina and Feighn [23] constructed a hyperbolic complexes on which Out(Fn) acts so that the action of the elements of the family I is loxodromic and satisfies the WPD condition.”
On hyperbolicity of free splitting and free factor complexes (2012, background): “e (quasi-isometric) complexes FFN and IN have inﬁnite diameter. Since the inclusion map ιabove is Lipschitz, this implies that FSN has inﬁnite diameter as well. A subsequent result of Bestvina-Feighn [3] implies that every fully irreducible element ϕ∈Out(FN) acts on FFN with positive asymptotic tran”
Automorphisms of graph products of groups from a geometric perspective (2018, background): “The situation is less clear for Aut(Fn): while it is known that Out(Fn) is acylindrically hyperbolic for n ≥ 2 [BF10], the case of Aut(Fn) seems to be open.”
Induced quasicocycles on groups with hyperbolically embedded subgroups (2012, result): “This general result applies in the following cases: (d1) G is the mapping class group of a punctured closed orientable surface and g is a pseudo-Anosov element [6]; (d2) G = Out(Fn) and g is a fully irreducible automorphism [5].”
GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES (2017, methodology): “Bestvina and Feighn [2010] proved that for every fully irreducible automorphism f 2 Out(Fn) there exists a hyperbolic graph such thatOut(Fn) acts on it and the action of f satisfies the weak proper discontinuity condition. Thus Out(Fn) is acylindrically hyperbolic by Theorem 2.14. (c) Groups acting ”