Geometry of the complex of curves and of Teichmüller space
By U. Hamenstaedt. 2005
88 citations recorded by the source corpus.
In this survey paper we give a proof of hyperbolicity of the complex of curves for a non-exceptional surface S of finite type combining ideas of Masur/Minsky and Bowditch. We also shortly discuss the relation between the geometry of the complex of curves and the geometry of Teichmueller space.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/340459ee5ab38240990737be45bac0ccceee235b
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In Geometry and Topology
- Saul Schleimer
- David Bachman
- Matt Clay
- J. Blanc
- Kasra Rafi
- Serge Cantat
- Maggy Tomova
- Msri Postdoctoral Fellow
Citations in the corpus
- 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.”
- Dynamical degrees of birational transformations of projective surfaces (2013, background): “3It also acts on the complex of curves of the surface, a metric space which is Gromov hyperbolic (see [31]).”
- Connected sums of unstabilized Heegaard splittings are unstabilized (2004, methodology): “The picture is reminiscent of the geodesic hierarchies of Masur and Minsky [10].”
- Uniform hyperbolicity of the graphs of curves (2012, unknown): “We will need the following fact about vertex cycles (see Hamenstädt [8] for a proof).”