Property (T) and actions on the real line

Abstract: This talk will focus on the class of countable groups admitting a faithful action on \(\mathbb{R}\) by orientation-preserving homeomorphisms. Equivalently, these are the groups that admit a left-invariant order. The main question that we will address is how Property (T) -an analytic property defined in terms of unitary representations- imposes restrictions on the kinds of action that a group can have on \(\mathbb{R}\).

The first part of the talk will be devoted to basic definitions and examples. In the second part, I will present a result that links the Lipschitz and Kazhdan constants associated to finite generating subsets.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar