Examples of Groups that are Measure Equivalent to the Free Group

Details Examples of Groups that are Measure Equivalent to the Free Group Examples of Groups that are Measure Equivalent to the Free Group

2005-03-09

arxiv.org/abs/math/0503181v2

Mathematics

Dynamical Systems

To appear in Ergodic Theory and Dynamical Systems

Scientific paper

Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable free-factor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group. We also present a quite extensive survey on results about Measure Equivalence for countable groups.

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