Higher Kazhdan projections, -Betti numbers and Baum–Connes conjectures
Kang Li
Friedrich-Alexander-Universität Erlangen-Nürnberg, GermanyPiotr Nowak
Institute of Mathematics of the Polish Academy of Sciences, Warszawa, PolandSanaz Pooya
Stockholm University, Sweden
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Abstract
We introduce higher-dimensional analogs of Kazhdan projections in matrix algebras over group -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 -theory classes. We apply the higher Kazhdan projections to establish a relation between -Betti numbers of a group and surjectivity of different Baum–Connes type assembly maps.
Cite this article
Kang Li, Piotr Nowak, Sanaz Pooya, Higher Kazhdan projections, -Betti numbers and Baum–Connes conjectures. J. Noncommut. Geom. 18 (2024), no. 1, pp. 313–336
DOI 10.4171/JNCG/529