Hyperbolicity of the complex of free factors

By M. Bestvina, Mark Feighn. 2011

159 citations recorded by the source corpus.

We develop the geometry of folding paths in Outer space and, as an application, prove that the complex of free factors of a free group of finite rank is hyperbolic.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c4d732e3f8c0d6afe76dbc83dade0619b5a38f0d

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

In Mathematical Physics

Citations in the corpus

Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, methodology): “ (or iwip, for brevity) if none of its non-trivial powers preserve the conjugacy class of a proper free factor of F n. Given F n, and a nite family I of iwip elements in Out(F n), Bestvina and Feighn [25, 26] constructed hyperbolic spaces on which Out(F n) acts so that the action of the elements of ”
Homotopy type of the complex of free factors of a free group (2018, background): “Most notably, Bestvina and Feighn in [2] showed that Fn is Gromov-hyperbolic, in analogy to Masur–Minsky’s hyperbolicity result for the curve complex of a surface [21].”
Hyperbolic extensions of free groups (2014, methodology): “This is their unfolding principle, which we state as the following lemma: Lemma 2.7 (Unfolding principle [BF2]) .”
On hyperbolicity of free splitting and free factor complexes (2012, methodology): “A subsequent result of Bestvina-Feighn [3] implies that every fully irreducible element ϕ ∈ Out(FN ) acts on FFN with positive asymptotic translation length (hence the same is true for the action of ϕ on FSN).”
Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-proper Settings (2014, background): “In the process we came to realize that a more natural domain for our inquiries was the much larger setting of semigroups acting on Gromov hyperbolic metric spaces – that way we could simultaneously answer our own questions about H and construct a theoretical framework for those who are interested in”
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces (2013, background): “ins in Banach spaces [88, Theorem 2.12] Arc graphs and curve graphs [41] and arc complexes [57, 47] of nitely punctured oriented surfaces Free splitting complexes [40, 47] and free factor complexes [9, 50, 47] 2.2. The boundary of a hyperbolic metric space. In this subsection, we dene the Gromov bou”