Higher Kazhdan projections, $\ell_2$-Betti numbers and Baum-Connes conjectures

Kang Li; Piotr W. Nowak; Sanaz Pooya

Higher Kazhdan projections, $\ell_2$-Betti numbers and Baum-Connes conjectures

Operator Algebras 2020-06-19 v2 Group Theory K-Theory and Homology

Authors: Kang Li , Piotr W. Nowak , Sanaz Pooya

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 $\ell_2$ -Betti numbers of a group and surjectivity of different Baum-Connes type assembly maps.

Keywords

kazhdan projections group c*-algebras roe algebras l2-betti numbers baum-connes conjecture k-theory

Cite

@article{arxiv.2006.09317,
  title  = {Higher Kazhdan projections, $\ell_2$-Betti numbers and Baum-Connes conjectures},
  author = {Kang Li and Piotr W. Nowak and Sanaz Pooya},
  journal= {arXiv preprint arXiv:2006.09317},
  year   = {2020}
}

Comments

Conclusion of Theorem 2 strengthened; typos corrected

Higher Kazhdan projections, $\ell_2$-Betti numbers and Baum-Connes conjectures

Abstract

Keywords

Cite

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