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Hyperbolic generalized triangle groups, property (T) and finite simple quotients

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GRA - Groups, representations and applications: new perspectives

It is a long-standing open problem in Geometric Group Theory to
determine whether all Gromov hyperbolic groups are residually finite.
Contributions of Olshanskii imply that, in order to answer this question
in the negative, it suffices to find a hyperbolic group that does not
admit finite simple quotients of arbitrarily large rank. In this talk, I
will report on efforts in identifying explicit candidates of such a
hyperbolic group, and explain a connection with Kazhdan's property (T).
This is partly based on an experimental case study on generalized
triangle groups, conducted jointly with Marston Conder, Marek Kaluba and
Stefan Witzel.




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