SOME COMPUTATIONS OF 1-COHOMOLOGY GROUPS AND CONSTRUCTION OF NON-ORBIT-EQUIVALENT ACTIONS
SOME COMPUTATIONS OF 1-COHOMOLOGY GROUPS AND CONSTRUCTION OF NON-ORBIT-EQUIVALENT ACTIONS
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1-上同调群的一些计算及非轨道等效作用的构造
DOI：
10.1017/s1474748006000016
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发表时间：
2004
影响因子：
0.9
通讯作者：
S. Popa
中科院分区：
文献类型：
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作者：
S. Popa
对于每个群G有一个具有相对性质（T）的无穷正规子群（例如，$G=H\times K$，其中$H$具有无限性质（T），$K$是任意的）和每个可数阿贝尔群$\varLambda$，我们在概率空间上构造$G$的自由遍历保测作用$\sigma_\varLambda$，使得$\sigma_\varLambda$的第一上同调群，$\ssm{H}^1（\sigma_\varLambda，G）$，等于$\text{Char}（G）\times\varLambda$。我们推导出$G$有不可数多的非稳定轨道等价作用量。我们还计算了1-上同调群，并证明了群的自由积存在“许多”非稳定轨道等价作用。
For each group $G$ having an infinite normal subgroup with the relative property (T) (e.g. $G=H\times K$, with $H$ infinite with property (T) and $K$ arbitrary) and each countable abelian group $\varLambda$ we construct free ergodic measure-preserving actions $\sigma_\varLambda$ of $G$ on the probability space such that the first cohomology group of $\sigma_\varLambda$, $\ssm{H}^1(\sigma_\varLambda,G)$, is equal to $\text{Char}(G)\times\varLambda$. We deduce that $G$ has uncountably many non-stably orbit-equivalent actions. We also calculate 1-cohomology groups and show existence of ‘many’ non-stably orbit-equivalent actions for free products of groups as above.