论文标题
统一ROE代数的度量空间和嵌入的粗大商
Coarse quotients of metric spaces and embeddings of uniform Roe algebras
论文作者
论文摘要
我们研究了均匀的ROE代数的嵌入，它们的代码域具有“较大范围”，以及与公制空间之间粗略的人的关系。除其他结果外，我们还表明，如果$ y $具有属性a，并且有一个嵌入$φ：\ mathrm {c}^*_ u（x）\ to \ mathrm {c}^*_ U（y）$带有“大型范围”，那么$φ（\ ell _ ell _ ell_ \ ell_ \ infty（x）$是一个Cartan subalge subalge subalgebra $ \ mathrm {c}^*_ u（y）$，然后有一个Bioxtive粗糙商$ x \ y $。这表明，从某种意义上说，$ y $的大规模几何形状由$ x $之一控制。例如，如果$ x $具有有限的渐近维度，那么$ y $也是如此。
We study embeddings of uniform Roe algebras which have "large range" in their codomain and the relation of those with coarse quotients between metric spaces. Among other results, we show that if $Y$ has property A and there is an embedding $Φ:\mathrm{C}^*_u(X)\to \mathrm{C}^*_u(Y)$ with "large range" and so that $Φ(\ell_\infty(X))$ is a Cartan subalgebra of $\mathrm{C}^*_u(Y)$, then there is a bijective coarse quotient $X\to Y$. This shows that the large scale geometry of $Y$ is, in some sense, controlled by the one of $X$. For instance, if $X$ has finite asymptotic dimension, so does $Y$.
