度量空间上余氏性质A的上同调刻画
A cohomological characterisation of Yu's Property A for metric spaces
摘要：
性质A由Yu引入作为顺从性的非等变模拟。奈杰尔·希格森提出了性质A是否存在同调特征的问题。本文通过构造度量空间X的群上同调和有界上同调的类似物，肯定地回答了Higson的问题，并证明了性质A等价于消失上同调.利用这些上同调理论，我们还给出了性质A在空间上存在渐近不变平均的一个刻画。
英文摘要：
Property A was introduced by Yu as a non-equivariant analogue of amenability. Nigel Higson posed the question of whether there is a homological characterisation of property A. In this paper we answer Higson's question affirmatively by constructing analogues of group cohomology and bounded cohomology for a metric space X, and show that property A is equivalent to vanishing cohomology. Using these cohomology theories we also give a characterisation of property A in terms of the existence of an asymptotically invariant mean on the space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
