Higher Kazhdan projections, ℓ₂-Betti numbers and Baum-Connes conjectures

2020/06/16 by Li, Kang, Nowak, Piotr W., Pooya, Sanaz · 2 citations
#FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2006.09317

Abstract

We introduce higher-dimensional analogs of Kazhdan projections in matrix algebras over group C^*-algebras and Roe algebras. These projections are constructed in the framework of cohomology with coefficients in unitary representations and in certain cases give rise to non-trivial K-theory classes. We apply the higher Kazhdan projections to establish a relation between ℓ₂-Betti numbers of a group and surjectivity of different Baum-Connes type assembly maps.

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• Euler characteristics, higher Kazhdan projections and delocalised ℓ²-Betti numbers
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