论文标题
轨道的同时学和卡勒刚度
Orbital cohomology and Kahler rigidity
论文作者
论文摘要
在$ 70 $的费尔德曼（Feldman）和摩尔（Moore）中，摩尔（Moore）定义了与Abelian波兰集团中与系数的可数等效关系相关的共同体。当等效关系是轨道关系时，那就是它是由可数组$γ$在标准borel概率$（x，μ）$上的量度保留动作引起的，考虑到Feldmann-Moore $ 1 $ - 酒体具有$ G $ - g $ - ceefficientions，time $ g $均可$ g $。后者的共同体以$ h^1（γ\ curvearrowright x; g）$表示，除了某些例外情况外，非常奇妙且难以计算。 在这份说明性论文中，当$γ$是有限的群体而$ g $是Hermitian Lie Group时，我们将把注意力集中在特定情况下。我们将在这种情况下给出一些最新的刚度结果，我们将看到如何使用这些结果来说明有关（某些子集的）轨道共同体。
In the late $70$'s Feldman and Moore defined the cohomology associated to a countable equivalence relation with coefficients in an Abelian Polish group. When the equivalence relation is the orbital one, that is it is induced by a measure preserving action of a countable group $Γ$ on a standard Borel probability space $(X,μ)$, it still makes sense to consider the Feldmann-Moore $1$-cohomology with $G$-coefficients, where this time $G$ can be any topological group. The latter cohomology, denoted by $H^1(Γ\curvearrowright X;G)$, is very misterious and hard to compute, except for some exceptional cases. In this expository paper we are going to focus our attention on the particular case when $Γ$ is a finitely generated group and $G$ is a Hermitian Lie group. We are going to give some recent rigidity results in this context and we will see how those results can be used to say something relevant about (some subsets of) the orbital cohomology.
