The free splitting complex of a free group I: Hyperbolicity

By M. Handel, Lee Mosher. 2011

101 citations recorded by the source corpus.

We prove that the free splitting complex of a finite rank free group, also known as Hatcher's sphere complex, is hyperbolic.

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

View Paper: https://www.semanticscholar.org/paper/ae33cf5074f263ef10e89766324e2974d26f76bc

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

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Citations in the corpus

The boundary of the complex of free factors (2012, methodology): “Kapovich-Rafi [KR] have shown that hyperbolicity of F can be deduced from the hyperbolicity of the free splitting complex, which was shown by Handel-Mosher [HM12], and an alternative proof of this was given by Hilion-Horbez [HH].”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “The recent papers [24] and [70] provides two other hyperbolic spaces on which Out(Fn) acts.”
The hyperbolicity of the sphere complex via surgery paths (2012, methodology): “In [10], Handel and Mosher have proved that the free splitting complex FSn for the free group Fn is Gromov hyperbolic.”
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces (2013, background): “perbolic metrics of uniform domains in Banach spaces [89, Theorem 2.12] • Arc graphs and curve graphs [43] and arc complexes [59, 49] of ﬁnitely punctured oriented surfaces • Free splitting complexes [42, 49] and free factor complexes [9, 52, 49] 2.2. The boundary of a hyperbolic metric space. In th”
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”
On hyperbolicity of free splitting and free factor complexes (2012, methodology): “We need the following technical notion which is a variant of the notion of a foldable map from the paper of Handel-Mosher [14].”
Hyperbolicity of the complex of free factors (2011, background): “We thank Michael Handel for pointing out the technique for proving the following lemma (see [14, Proposition 8.1]).”
Uniform hyperbolicity of the curve graph via surgery sequences (2013, methodology): “The splitting graph, another variant of the curve graph for the free group, was recently shown to be hyperbolic by Handel and Mosher [9].”