具有不同基本群的II $_1$因子和等价关系
II$_1$ factors and equivalence relations with distinct fundamental groups
摘要：
我们构造了一个群测度空间II的$_1$因子，它具有两个非共轭的Cartan子代数.我们证明了II $_1$因子的基本群是平凡的，而与第二Cartan子代数相关的等价关系的基本群是非平凡的.这并不荒谬，因为第二个嘉当包含体被一个2-上圈扭曲。
英文摘要：
We construct a group measure space II$_1$ factor that has two non-conjugate Cartan subalgebras. We show that the fundamental group of the II$_1$ factor is trivial, while the fundamental group of the equivalence relation associated with the second Cartan subalgebra is non-trivial. This is not absurd as the second Cartan inclusion is twisted by a 2-cocycle.
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。
