Kleinian convex cocompact subgroups of mapping class groups- Spencer Dowdall

Conference Title: GEAR Retreat 2012 Theme: Geometric Structures and Teichmuller Spaces (3 of 5) Title: Kleinian convex cocompact subgroups of mapping class groups Speaker: Spencer Dowdall, Univ. of Illiinois at Urbana-Champaign; Date and Time: Friday August 10, 14:00 Description: Convex cocompact subgroups of mapping class groups, as introduced by Farb and Mosher, are subgroups whose action on Teichmuller space is analogous to that of convex cocompact Kleinian groups acting on H3. In this talk I will describe a setting in which there is a concrete connection between these two notions of convex cocompactness: Because of the Birman exact sequence, fibered hyperbolic 3-manifold groups give many ways to realize Kleinian groups as subgroups of mapping class groups. Expanding on earlier work of Kent-Leininger-Schleimer, I will explain a result that certain subgroups of these 3-manifold groups which are convex cocompact in the Kleinian sense are also convex cocompact as subgroups of the mapping class group. This is joint work with Richard Kent and Christopher Leininger. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Prof. Spencer Dowdall, in this GEAR Retreat 2012 session on Geometric Structures and Teichmuller Spaces, will describe a setting in which there is a concrete connection between these two notions of convex cocompactness.