Topological properties of full groups
Topological properties of full groups
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全群的拓扑性质
DOI：
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发表时间：
2009
影响因子：
0.9
通讯作者：
T. Tsankov
中科院分区：
文献类型：
--
作者：
J. Kittrell;T. Tsankov
摘要研究可数保测度等价关系的全群。我们的主要结果包括：它们都同胚于可分Hilbert空间，从遍历满群到可分群的同态都是连续的。我们还发现边界的最小数量的拓扑生成器（元素生成一个稠密的子群）的全组，使我们能够区分全组的等价关系所产生的自由，遍历行动的自由组Fm和Fn，如果m和n是足够远的。我们还证明了遍历等价关系是由一个拓扑生成群的作用生成的，当且仅当它的全群是拓扑生成的。
Abstract We study full groups of countable, measure-preserving equivalence relations. Our main results include that they are all homeomorphic to the separable Hilbert space and that every homomorphism from an ergodic full group to a separable group is continuous. We also find bounds for the minimal number of topological generators (elements generating a dense subgroup) of full groups allowing us to distinguish between full groups of equivalence relations generated by free, ergodic actions of the free groups Fm and Fn if m and n are sufficiently far apart. We also show that an ergodic equivalence relation is generated by an action of a finitely generated group if an only if its full group is topologically finitely generated.