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Examples of groups that are measure equivalent to the free group

Published online by Cambridge University Press:  07 October 2005

D. GABORIAU
D. GABORIAU
Affiliation:
UMPA, UMR CNRS 5669, ENS-Lyon, 69364 Lyon Cedex 7, France (e-mail: [email protected])
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Abstract

Measure equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field has grown considerably over the past few years, developing tools to distinguish between different ME classes of countable groups. On the other hand, constructions of ME 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 ME for countable groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 6 , December 2005 , pp. 1809 - 1827
Copyright
2005 Cambridge University Press

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