Measured Asymptotic Expanders and Rigidity for Roe Algebras

Li K, Spakula J, Zhang J (2022)

Publication Type: Journal article

Publication year: 2022


DOI: 10.1093/imrn/rnac242


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.

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Li, K., Spakula, J., & Zhang, J. (2022). Measured Asymptotic Expanders and Rigidity for Roe Algebras. International Mathematics Research Notices.


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

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