Coarse Baum-Connes conjecture and rigidity for Roe algebras

Braga BM, Chung YC, Li K (2020)


Publication Type: Journal article

Publication year: 2020

Journal

Book Volume: 279

Article Number: 108728

Journal Issue: 9

DOI: 10.1016/j.jfa.2020.108728

Abstract

In this paper, we connect the rigidity problem and the coarse Baum-Connes conjecture for Roe algebras. In particular, we show that if X and Y are two uniformly locally finite metric spaces such that their Roe algebras are ⁎-isomorphic, then X and Y are coarsely equivalent provided either X or Y satisfies the coarse Baum-Connes conjecture with coefficients. It is well-known that coarse embeddability into a Hilbert space implies the coarse Baum-Connes conjecture with coefficients. On the other hand, we provide a new example of a finitely generated group satisfying the coarse Baum-Connes conjecture with coefficients but which does not coarsely embed into a Hilbert space.

Authors with CRIS profile

Involved external institutions

How to cite

APA:

Braga, B.M., Chung, Y.C., & Li, K. (2020). Coarse Baum-Connes conjecture and rigidity for Roe algebras. Journal of Functional Analysis, 279(9). https://dx.doi.org/10.1016/j.jfa.2020.108728

MLA:

Braga, Bruno M., Yeong Chyuan Chung, and Kang Li. "Coarse Baum-Connes conjecture and rigidity for Roe algebras." Journal of Functional Analysis 279.9 (2020).

BibTeX: Download