Rigidity of amalgamated free products in measure equivalence

Abstract

A discrete countable group Γis said to be ME rigid if any discrete countable group that is measure equivalent to Γis virtually isomorphic to Γ. 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.

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

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