Examples of groups that are measure equivalent to the free group
Ergodic Theory & Dynam. Systems, 25 (2005), no. 6, 1809-1827.
Link to Ergodic
Theory and Dynamical Systems
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Also ArXiV: http://arxiv.org/abs/math/0503181,
HAL (CNRS): http://hal.ccsd.cnrs.fr/ccsd-00004408
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.
Last modification: May 20, 2005