Higher Kazhdan projections, `2-Betti numbers and Baum–Connes conjectures

Li K, Nowak PW, Pooya S (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Journal of Noncommutative Geometry European Mathematical Society

Book Volume: 18

Pages Range: 313-336

Journal Issue: 1

DOI: 10.4171/JNCG/529

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 `2-Betti numbers of a group and surjectivity of different Baum–Connes type assembly maps.

Authors with CRIS profile

Kang Li Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

Mathematical Institute of the Polish Academy of Sciences PL Poland (PL) Stockholm University / Stockholms universitet SE Sweden (SE)

How to cite

APA:

Li, K., Nowak, P.W., & Pooya, S. (2024). Higher Kazhdan projections, `2-Betti numbers and Baum–Connes conjectures. Journal of Noncommutative Geometry, 18(1), 313-336. https://doi.org/10.4171/JNCG/529

MLA:

Li, Kang, Piotr W. Nowak, and Sanaz Pooya. "Higher Kazhdan projections, `2-Betti numbers and Baum–Connes conjectures." Journal of Noncommutative Geometry 18.1 (2024): 313-336.

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