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
University of Virginia (UVA)
United States (USA) (US)
Polska Akademia Nauk (PAN) / Polish Academy of Sciences
Poland (PL)
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
United States (USA) (US)
Polska Akademia Nauk (PAN) / Polish Academy of Sciences
Poland (PL)
Mathematical Institute of the Polish Academy of Sciences
Poland (PL)
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).
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