Rigidity of amalgamated free products in measure equivalence

Details Rigidity of amalgamated free products in measure equivalence Rigidity of amalgamated free products in measure equivalence

2009-02-17

arxiv.org/abs/0902.2888v4

J.Topol. 4 (2011) 687-735

Mathematics

Group Theory

51 pages, Theorem 1.5 (a) and Proposition 9.5 modified

Scientific paper

10.1112/jtopol/jtr012

A discrete countable group \Gamma is said to be ME rigid if any discrete countable group that is measure equivalent to \Gamma is virtually isomorphic to \Gamma. In this paper, we construct ME rigid groups by amalgamating two groups satisfying rigidity in a sense of measure equivalence. A class of amalgamated free products is introduced, and discrete countable groups which are measure equivalent to a group in that class are investigated.

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