Asymptotic Geometry of the Mapping Class Group and Teichmuller Space

By Jason A. Behrstock. 2005

215 citations recorded by the source corpus.

In this work, we study the asymptotic geometry of the mapping class group and Teichmuller space. We introduce tools for analyzing the geometry of “projection” maps from these spaces to curve complexes of subsurfaces; from this we obtain information concerning the topology of their asymptotic cones. We deduce several applications of this analysis. One of which is that the asymptotic cone of the mapping class group.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/22aff9116bc14b7b548527ae6a4c55922cc3f3ef

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hierarchically hyperbolic spaces II: Combination theorems and the distance formula (2015, methodology): “These projections are required to obey consistency conditions modeled on the inequality identi ed by Behrstock in [Beh06], as well as a version of the bounded geodesic image theorem and large link lemma of [MM00], among other conditions.”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “Examples of constricted groups include relatively hyperbolic groups [53], all but finitely many mapping class groups [17], Out(Fn) for n ≥ 2 [3], and many “exotic” groups such as Tarski Monsters [103].”
Hierarchically hyperbolic spaces I: curve complexes for cubical groups (2014, background): “The formulation here is very close to that in the mapping class group, see [Beh06] and [BKMM12].”