Higher Kazhdan projections and delocalised ${\ell }^2$-Betti numbers

Abstract

We provide an explicit description of the K-classes of higher Kazhdan projections in degrees greater than 0 for specific free product groups and Cartesian product groups. Employing this description, we obtain new calculations of Lott's delocalised ${\ell }^2$-Betti numbers. Notably, we establish the first non-vanishing results for infinite groups.

19 pages, Accepted for publication in the Annals of K-theory