The maximal coarse Baum–Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space
The maximal coarse Baum–Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space
复制标题
允许纤维粗嵌入希尔伯特空间的空间的最大粗鲍姆康内斯猜想
DOI：
10.1016/j.aim.2013.09.003
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发表时间：
2013
影响因子：
1.7
通讯作者：
Guoliang Yu
中科院分区：
文献类型：
--
作者：
Xiaoman Chen;Qin Wang;Guoliang Yu
本文在度量空间中引入了Hilbert空间的广义粗嵌入概念，它是Gromov的广义粗嵌入概念在Hilbert空间中的推广.事实证明，一个大类的扩展图承认这样的嵌入。本文证明了极大粗Baum-Connes猜想对具有有界几何的度量空间成立，且该度量空间允许向Hilbert空间中嵌入一个极大粗嵌入.
We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromovʼs notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum–Connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into Hilbert space.