Speaker: Ryo Toyota (UCPH)
Title: Geometric property (T) for warped cones
Abstract: Warped cone is a metric space associated to a group action on a compact metric space. Notably, the expanding property of the warped cone can be characterized by the spectral gap property of the underlying action. Geometric property (T) is a coarse geometric analogue of Kazhdan's property (T), which is strictly stronger than the expanding property. It was conjectured that the warped cone associated to an ergodic action by a group with Kazhdan's property (T) should have geometric property (T).
In this talk, I will present counterexamples to this conjecture. More generally, I will explain why a free isometric action on a compact Riemannian manifold never gives rise to a warped cone with geometric property (T). Part of this talk is based on a joint work with Jintao Deng.