Higher Kazhdan projections and their K-theory

Sanaz Pooya (University of Potsdam)

Thursday 12th February 16:00-17:00
Maths 116

Abstract

Many important properties of groups can be detected by studying the algebraic structures naturally associated with them. A well-known example is Kazhdan’s property (T), which can be characterised by a special element called a Kazhdan projection. It lives in the universal group C*-algebra and is therefore of an operator algebraic nature. In this talk, I will describe higher-dimensional analogues of this construction called higher Kazhdan projections. These capture topological information beyond the classical rigidity phenomena associated with property (T) groups and can exist even in groups that do not have property (T). I will then explain how higher Kazhdan projections naturally give rise to K-theory classes and how numerical invariants can be extracted from them via trace pairings. This framework provides new tools for studying delocalised l2-Betti numbers and leads to explicit computations for groups.

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