A new boundary for the mapping class group
Geometry of mapping class groups and Out(Fn) October 25, 2016 - October 28, 2016
Location: SLMath: Eisenbud Auditorium
Mapping Class Group
Hierarchically hyperbolic space
HHS
Boundary
Cannon-Thurston map
35Q92 - PDEs in connection with biology, chemistry and other natural sciences
00A35 - Methodology of mathematics {For mathematics education, see 97-XX}
01-11 - Research data for problems pertaining to history and biography
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.
Durham.Notes
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