Examples of groups that are measure equivalent to the free group

By Damien Gaboriau. Ergodic Theory and Dynamical Systems, 2005

78 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3dd1324eb8ce714a197a09337dd6e5cefe9039c8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Adrian Ioana
2. Thomas Sinclair
3. Sorin Popa
4. J. Peterson
5. S. Vaes
6. Y. Kida
7. A. Furman
8. I. Chifan

In Mathematical Physics

1. Adrian Ioana
2. Thomas Sinclair
3. Sorin Popa
4. S. Vaes
5. J. Peterson
6. I. Chifan
7. Cyril Houdayer
8. A. Furman

Citations in the corpus

• On cocycle superrigidity for Gaussian actions (2009, background): “Examples of groups which are orbit equivalent to a free group can be found in [4, 17].”
• The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, background): “The references [29], [95] are quite detailed surveys in which various recent progress about measure equivalence are treated.”
• Amalgamated free products of weakly rigid factors and calculation of their symmetry groups (2005, background): “By perturbing α by Ad(w0) for an appropriate w0 ∈ U(R2) we may thus assume αR2 = idR2 . Thus α is given by a character of G2 . �”
• Measure equivalence rigidity of the mapping class group (2006, background): “The first magnificent result about orbit equivalence is due to Ornstein-Weiss [33] following Dye [5], [6] and it can be stated in terms of measure equivalence as follows: a discrete group is measure equivalent to Z if and only if it is an infinite amenable group.”