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Triangles of groups, property (T), expanders and special quotients

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If you have a question about this talk, please contact Maurice Chiodo .

I’ll explain an application of the existence of certain families of expanders to an open problem in geometric group theory. To be precise, I’ll use families of expanders to construct families of hyperbolic triangles of groups with property (T). In particular, this gives explicit families of examples of hyperbolic groups which cannot be cubulated. We deduce that the hypotheses of Wise’s celebrated Malnormal Special Quotient Theorem cannot be weakened, answering a question of Agol. This is joint with with Alex Lubotzky, Jason Manning and Peter Varju.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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