Train tracks and the geometry of the complex of curves

By U. Hamenstaedt. 2005

431 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/92b027324090ab1a61bca3341d2b50c6fc7ebc37

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Citations in the corpus

THE CLASSIFICATION OF KLEINIAN SURFACE GROUPS, II: THE ENDING LAMINATION CONJECTURE (2004, unknown): “) We recall from Masur-Minsky [45] that C(X) is δ-hyperbolic (see also Bowditch [15] for a new proof) and from Klarreich [40] (see also Hamenstadt [31] for an alternate proof) that its Gromov boundary ∂C(X) can be identified with the set EL(X) of minimal filling geodesic laminations on X, with the t”
Acylindrically hyperbolic groups (2013, methodology): “For all other values of ( g, p ) this follows from hyperbolicity of the curve complex C (Σ g,p ) of Σ g,p ﬁrst proved by Mazur and Minsky [35] and acylindricity of the action of MCG (Σ g,p ) on C (Σ g,p ), which is due to Bowditch [8].”
Uniform hyperbolicity of the graphs of curves (2012, unknown): “We note that this constant B also occurs in the proof of the quasiconvexity of the disk set by Masur and Minsky in [14]. proof : We can assume that τ is generic and birecurrent since for any train track τ , there exists a generic birecurrent track τ ′ such that P (τ) = P (τ ′) (see [17]).”
Big Mapping Class Groups: An Overview (2020, background): “In this direction, the following is a seminal theorem of Masur–Minsky [87]: [87]) .”
Geometric Intersection Number and analogues of the Curve Complex for free groups (2007, unknown): “Masur and Minsky [35] and Hempel [21] established that the curve graph has infinite diameter.”
Coarse and synthetic Weil–Petersson geometry: quasi-flats, geodesics and relative hyperbolicity (2007, background): “We remark that the following statement has been obtained independently (and for all surfaces S) by work of Behrstock and Minsky (see [BM]).”
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.”
Growth tight actions (2014, background): “However, Masur and Minsky [38] use ‘contracting’ in the sense of Definition 6.1, as do subsequent papers on the geometry of the mappping class group.”
Measure equivalence rigidity of the mapping class group (2006, background): “Moreover, when C is equipped with a natural combinatorial metric, it is hyperbolic in the sense of Gromov (see [29]).”
GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES (2017, unknown): “It is also observed by Osin [2010] that such a group cannot be constructed as a limit of hyperbolic groups; this justifies the use of small cancellation theory in the more general settings.”
The Farrell–Jones Conjecture for mapping class groups (2016, methodology): “The following is a celebrated theorem of Masur and Minsky.”