Geometric property (T) of warped cones
Ryo Toyota (Texas A&M University)
Thursday 5th March 16:00-17:00
Maths 116
Abstract
Warped cones are metric spaces associated with actions of discrete groups on compact metric spaces, whose large-scale geometric properties reflect the dynamical properties of the underlying action. It is known that the associated warped cone forms an expander if and only if the underlying action has a spectral gap.
Geometric property (T) is a strengthening of the expansion property, and it has been an open problem whether the warped cone associated with an ergodic action of a discrete group with Kazhdan’s Property (T) has geometric property (T).
In this talk, we exhibit a counterexample to this question. Our example is also the first example of a superexpander without geometric property (T).
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