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

Sanaz Pooya and Hang Wang
Vol. 11 (2026), No. 3, 395–418
DOI: 10.2140/akt.2026.11.395
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 ℓ2-Betti numbers for groups. Notably, we establish the first nonvanishing results for infinite groups.

Keywords
higher Kazhdan projection, delocalised $\ell^2$-Betti number, delocalised trace, Puschnigg subalgebra
Mathematical Subject Classification
Primary: 19D55, 20F65, 46L80
Milestones
Received: 23 May 2024
Revised: 25 February 2026
Accepted: 6 April 2026
Published: 19 May 2026
Authors
Sanaz Pooya
Institute of Mathematics
University of Potsdam
Potsdam
Germany
Hang Wang
School of Mathematical Sciences
East China Normal University
Shanghai
China
© 2026 MSP (Mathematical Sciences Publishers).