A brief introduction to amenable equivalence relations
A brief introduction to amenable equivalence relations
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简单介绍顺应的等价关系
DOI：
10.1090/conm/752/15134
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Moore, Justin Tatch
中科院分区：
文献类型：
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作者：
Moore, Justin Tatch
服从等价关系的概念是由Zimmer在分析遍历理论中轨道等价关系的过程中提出的(见[12])。最近，它在莫诺德引人注目的不包含非交换自由子群的不可从群的例子家族中扮演了重要的角色。如果A是R的一个子环，则定义H(A)是实投影线的所有分段PSL2(A)同胚群，它们都将点固定在无穷远。定理1.1[17]如果A是R的任何稠密子环，则H(A)是不可服从的。此外，如果f，g∈H(R)，则〈f，g〉是亚交换的，或者包含无限秩自由交换子群。特别地，H(R)不包含非交换自由子群。
The notion of an amenable equivalence relation was introduced by Zimmer in the course of his analysis of orbit equivalence relations in ergodic theory (see [12]). More recently it played an important role in Monod’s striking family of examples of nonamenable groups which do not contain nonabelian free subgroups. If A is a subring of R, define H (A) to be the group of all piecewise PSL2 (A) homeomorphisms of the real projective line which fix the point at infinity.Theorem 1.1.[17] If A is any dense subring of R, then H (A) is nonamenable. Moreover, if f, g∈ H (R), then either〈 f, g〉 is metabelian or else contains an infinite rank free abelian subgroup. In particular, H (R) does not contain a nonabelian free subgroup.