Measured Asymptotic Expanders and Rigidity for Roe Algebras

Li K, Spakula J, Zhang J (2022)

Publication Type: Journal article

Publication year: 2022

Journal

International Mathematics Research Notices Oxford University Press (OUP): Policy H - Oxford Open Option A

DOI: 10.1093/imrn/rnac242

Abstract

In this paper, we give a new geometric condition in terms of measured asymptotic expanders to ensure rigidity of Roe algebras. Consequently, we obtain the rigidity for all bounded geometry spaces that coarsely embed into some L-p-space for p is an element of [1, infinity). Moreover, we also verify rigidity for the box spaces constructed by Arzhantseva-Tessera and Delabie-Khukhro even though they do not coarsely embed into any L-p-space. The key step in our proof of rigidity is showing that a block-rank-one (ghost) projection on a sparse space X belongs to the Roe algebra C*(X) if and only if X consists of (ghostly) measured asymptotic expanders. As a by-product, we also deduce that ghostly measured asymptotic expanders are new sources of counterexamples to the coarse Baum-Connes conjecture.

Authors with CRIS profile

Kang Li Juniorprofessur für Mathematik (Darstellungstheorie und Operatoralgebren)

Involved external institutions

University of Southampton GB United Kingdom (GB) Fudan University / 复旦大学 CN China (CN)

How to cite

APA:

Li, K., Spakula, J., & Zhang, J. (2022). Measured Asymptotic Expanders and Rigidity for Roe Algebras. International Mathematics Research Notices. https://dx.doi.org/10.1093/imrn/rnac242

MLA:

Li, Kang, Jan Spakula, and Jiawen Zhang. "Measured Asymptotic Expanders and Rigidity for Roe Algebras." International Mathematics Research Notices (2022).

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