论文标题
SOFIC近似和定量测量耦合
Sofic approximations and quantitative measure couplings
论文作者
论文摘要
格罗莫夫（Gromov）引入了测量等效性，作为准时测量法的测量类似物。与后者不同，测量等效性并不能保留群体的大规模几何形状，并且在可及世界中恰好非常灵活。实际上，Ornstein-Weiss定理表明，所有无限可数的群体均与整数群相等。为了完善这种对等关系并使其响应几何形状，Delabie，Koivisto，LeMaître和Tessera引入了量度等效性的定量版本。他们还定义了这个概念的轻松版本，称为定量度量亚组耦合。在本文中，我们提出要回答量化的反问题（在lamplighter组的情况下，找到一个与规定的量化量的量度亚组耦合的组）。
Measure equivalence was introduced by Gromov as a measured analogue of quasi-isometry. Unlike the latter, measure equivalence does not preserve the large scale geometry of groups and happens to be very flexible in the amenable world. Indeed the Ornstein-Weiss theorem shows that all infinite countable amenable groups are measure equivalent to the group of integers. To refine this equivalence relation and make it responsive to geometry, Delabie, Koivisto, Le Maître and Tessera introduced a quantitative version of measure equivalence. They also defined a relaxed version of this notion called quantitative measure subgroup coupling. In this article we offer to answer the inverse problem of the quantification (find a group admitting a measure subgroup coupling with a prescribed group with prescribed quantification) in the case of the lamplighter group.
