Gromov’s measure equivalence and rigidity of higher rank lattices

Gromov’s measure equivalence and rigidity of higher rank lattices
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格罗莫夫测量高阶格的等价性和刚性

DOI：
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发表时间：
1999
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通讯作者：
A. Furman
A. Furman
中科院分区：
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文献类型：
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作者：
A. Furman

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研究了可数群的测度等价的概念。ME是由Gromov作为准等距的测度论类比引入的。同一局部紧群中的所有格都是度量等价的；这是这一概念的动机之一。本文的主要结果是高秩格的ME刚性：任何从ME到高阶单李群G中的格的可数群都可公度到G中的格。
In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the motivations for this notion. The main result of this paper is ME rigidity of higher rank lattices: any countable group which is ME to a lattice in a simple Lie group G of higher rank, is commensurable to a lattice in G.