Topology & Geometric Group Theory Seminar

Fall 2009

1:30 – 2:30, Malott 203

Tuesday, September 8

Jason Manning, University at Buffalo

Residual finiteness and separability of quasiconvex subgroups

It is unknown whether there exists a hyperbolic group which is not residually finite. Under the assumption that there is no such group, we deduce the separability of all quasiconvex subgroups of hyperbolic and (a class of) relatively hyperbolic groups. The main tools are relatively hyperbolic Dehn filling and (in the case of relatively hyperbolic groups) a combination theorem of Martinez-Pedroza. Part of this work is joint with Ian Agol and Daniel Groves; the rest is joint with Eduardo Martinez-Pedroza.

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