Intersection numbers and the hyperbolicity of the curve complex

By Brian H. Bowditch. 2006

171 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/edfcfac556d927cb1a5c5f1be5c97f954c5e16ed

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Shadows Of Mapping Class Groups: Capturing Convex Cocompactness (2005, unknown): “1 of [44], see also [11], C(S) is δ ′–hyperbolic for someδ ′.”
The geometry of the disk complex (2010, background): “We may now state a first answer to Bowditch’s question.”
Transitivity degrees of countable groups and acylindrical hyperbolicity (2015, background): “Mapping class groups of non-exceptional surfaces are acylindrically hyperbolic since they act acylindrically on the corresponding curve complexes, which are hyperbolic [37, 11]; mapping class groups of exceptional surfaces are either finite or non-virtually cyclic and hyperbolic.”
Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “In fact, acylindrically hyperbolic groups were implicitly studied by Bestvina and Fujiwara [17], Bowditch [18], Hamenstädt [43], Dahmani et al.”
Uniform hyperbolicity of the curve graph via surgery sequences (2013, methodology): “After the original paper of Masur and Minsky, Bowditch [4] and Hamenstädt [8] also gave proofs of the hyperbolicity of the curve graph.”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “The following lemma is due to Masur-Minsky [91] and Bowditch [28, 29].”
A hyperbolic Out(F_n)-complex (2008, background): “en small enough then Φ is coarsely onto. Proof. Let (p1,p2,p3) be a triple in M. Scale them so that all 3 intersection numbers are equal, say to 1. Then by Bowditch’s lemma (see Lemmas 5.1 and 5.3 of [Bow06], or for another exposition see 8 [BF07, Lemma 5.7]) there is a curve a such that I(a,pi) ≤ R”
On metric relative hyperbolicity (2012, methodology): “trans(x;y) coarsely coincides with the set of transient points on a geodesic from xto y. There are a few variations of the Guessing Geodesics Lemma for hyperbolic spaces, the rst of which appeared in [Bow06], where it is used to show hyperbolicity of curve complexes. Our formulation is closer to tha”
Geometry of the complex of curves and of Teichmüller space (2005, methodology): “On the other hand, by construction the minimal length with respect to this metric of a curve in the free homotopy class of γ is bounded from above by 2max{ai(α, γ), i(β, γ)/ai(α, β)} and therefore the core curve δ of the annulus has the properties stated in the first part of our lemma (see [2]).”
Acylindrically hyperbolic groups (2013, background): “lues of (g;p) this follows from hyperbolicity of the curve complex C( g;p) of g;prst proved by Mazur and Minsky [33] and acylindricity of the action of MCG( g;p) on C( g;p), which is due to Bowditch [8]. (b)Let n2 and let F n be the free group of rank n. Bestvina and Feighn [6] proved that for every”
Train tracks and the geometry of the complex of curves (2005, methodology): “…by URSULA HAMENST¨ADT construction the minimal length with respect to this metric of a curve in the free homotopy class of γ is bounded from above by 2 max{ai(α, γ), i(β, γ)/ai(α, β)} and therefore the core curve δ of the annulus has the properties stated in the first part of our lemma (see [2]).”