Measured Asymptotic Expanders and Rigidity for Roe Algebras
Measured Asymptotic Expanders and Rigidity for Roe Algebras
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Roe 代数的测量渐近展开式和刚性
DOI：
10.1093/imrn/rnac242
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发表时间：
2023
影响因子：
1
通讯作者：
Li K
中科院分区：
文献类型：
--
作者：
Li K
本文利用度量渐近展开子给出了Roe代数刚性的一个新的几何条件。因此，我们得到了所有有界几何空间的刚性，粗嵌入到一些空间。此外，我们还证明了Arzhantseva-Tessera和Delabie-Khukhro构造的盒空间的刚性，即使它们不粗嵌入任何空间。在我们的刚性证明的关键步骤是表明，一个块秩一（幽灵）的稀疏空间上的投影属于Roe代数，如果只有当组成（幽灵）测量渐近扩张。作为一个副产品，我们还推断，幽灵测量渐近展开是新的来源的反例粗鲍姆-康纳斯猜想。
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-space for. Moreover, we also verify rigidity for the box spaces constructed by Arzhantseva–Tessera and Delabie–Khukhro even though they donotcoarsely embed into any-space. The key step in our proof of rigidity is showing that a block-rank-one (ghost) projection on a sparse spacebelongs to the Roe algebraif and only ifconsists 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.