Geometric property (T) on warped cones

Ryo Toyota  (Texas A&M University)

10:00-11:00, June 11, 2026   Science Building A503

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 expanding 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 negatively answer this question. Our example is also the first example of a super-expander without geometric property (T).

About the speaker:

Attachments: