Shadows Of Mapping Class Groups: Capturing Convex Cocompactness

By Richard P. Kent, Christopher J. Leininger. 2005

128 citations recorded by the source corpus.

Abstract.We strengthen the analogy between convex cocompact Kleinian groups and convex cocompact subgroups of the mapping class group of a surface in the sense of B. Farb and L. Mosher.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a2183132d7da6c279753a5e717ab960d4863d7e0

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A recipe for short-word pseudo-Anosovs (2010, background): “oved these are common in mapping class groups of closed surfaces, and Kent and Leininger include a new proof which also works for non-closed surfaces: Theorem 3.11 (Abundance of Schottky groups [FM], [KL08a]). Given a nite set of pseudo-Anosovs fg1;g2;:::gkgwhich are independent (i.e., no pairs of p”
Almost filling laminations and the connectivity of ending lamination space (2008, background): “Peter Storm conjectured that ∂C(S) is path connected if S is any other finite type hyperbolic surface. See Question 10, [ KL ].”
The geometry of right angled Artin subgroups of mapping class groups (2010, background): “Given an arbitrary set of elements f1, . . . , fn ∈ Mod(S), we cannot expect that they generate a free group upon raising to sufficiently high powers.”
Boundaries and automorphisms of hierarchically hyperbolic spaces (2016, background): “Importantly, they satisfy several strong equivalent characterizations, which we state in the following theorem-definition with parts due variously to Farb-Mosher [FM02], Hamenstädt [Ham05], Kent-Leininger [KL08], and the first author with Taylor [DT15]:”