A measure-conjugacy invariant for free group actions

By Lewis Bowen. 2008

86 citations recorded by the source corpus.

This paper introduces a new measure-conjugacy invariant for actions of free groups. Using this invariant, it is shown that two Bernoulli shifts over a finitely generated free group are measurably conjugate if and only if their base measures have the same entropy. This answers a question of Ornstein and Weiss.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7d0d5e797075680eb762d3e466d70f1ba231b449

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In Computational Theory and Mathematics

1. Adrian Ioana

In Geometry and Topology

1. Adrian Ioana
2. S. Vaes
3. Sorin Popa
4. J. Peterson
5. Damien Gaboriau
6. Thomas Sinclair
7. A. Furman

In Mathematical Physics

1. Adrian Ioana
2. S. Vaes
3. Sorin Popa
4. Mihaita Berbec
5. J. Peterson
6. Thomas Sinclair
7. Damien Gaboriau
8. A. Furman

Citations in the corpus

• RIGIDITY FOR VON NEUMANN ALGEBRAS (2017, background): “oes not hold for arbitrary non-amenable groups. Indeed, if n ≥2, then the Bernoulli actions F n y (XFn 0 ,µ Fn 0 ) of F n are completely classified up to conjugacy by the entropy of base space (X0,µ0) [Bo08]; on the other hand, all Bernoulli actions of F n are orbit equivalent [Bo09]. 5. Orbit equiva”