Orbit equivalence, coinduced actions and free products

2009/06/24 by Lewis Bowen, Bowen, Lewis
Mathematics · #37A20 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0906.4573

openalex publication_date 2009/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The following result is proven. Let G₁ \cc^T₁ (X₁,μ₁) and G₂ \cc^T₂ (X₂,μ₂) be orbit-equivalent, essentially free, probability measure preserving actions of countable groups G₁ and G₂. Let H be any countable group. For i=1,2, let Γ_i = G_i *H be the free product. Then the actions of Γ₁ and Γ₂ coinduced from T₁ and T₂ are orbit-equivalent. As an application, it is shown that if Γ is a free group, then all nontrivial Bernoulli shifts over Γ are orbit-equivalent.

Citations

• A survey of Measured Group Theory
• On Groups of Measure Preserving Transformations. I
• Orbit inequivalent actions for groups containing a copy of \Bbb F₂

Related

• Stable orbit equivalence of Bernoulli shifts over free groups
• Orbit inequivalent actions of non-amenable groups
• Weak density of orbit equivalence classes and free products of infinite abelian groups
• Approximate equivalence of actions
• Orbit Equivalence and Measured Group Theory