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A new boundary for the mapping class group

Geometry of mapping class groups and Out(Fn) October 25, 2016 - October 28, 2016

October 28, 2016 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Matthew Durham (University of Michigan)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Mapping Class Group

  • Hierarchically hyperbolic space

  • HHS

  • Boundary

  • Cannon-Thurston map

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video
Technical Difficulty
Due to technical difficulty, no video is available.
Abstract

Using the framework of hierarchical hyperbolicity, we introduce a new compactification of the mapping class group which possesses the robust dynamical features of Thurston's compactification of Teichmuller space but is better suited for studying the asymptotics of subgroups.  As an application, we define a notion of geometrical finiteness for subgroups of mapping class groups and prove that several well-studied classes of subgroups are geometrically finite.  This is joint work with Mark Hagen and Alessandro Sisto.

Supplements
27145?type=thumb Durham.Notes 169 KB application/pdf Download