JournalsggdVol. 5, No. 1pp. 1–15

Orbit equivalence, coinduced actions and free products

  • Lewis Bowen

    The University of Texas at Austin, USA
Orbit equivalence, coinduced actions and free products cover

Abstract

The following result is proven. Let G1T1(X1,μ1)G_1 \curvearrowright^{T_1} (X_1,\mu_1) and G2T2(X2,μ2)G_2 \curvearrowright^{T_2} (X_2,\mu_2) be orbit equivalent (OE), essentially free, probability measure preserving actions of countable groups G1G_1 and G2G_2. Let HH be any countable group. For i=1,2i=1,2, let Γi=GiH\Gamma_i = G_i *H be the free product. Then the actions of Γ1\Gamma_1 and Γ2\Gamma_2 coinduced from T1T_1 and T2T_2 are OE. As an application, it is shown that if Γ\Gamma is a free group, then all nontrivial Bernoulli shifts over Γ\Gamma are OE.

Cite this article

Lewis Bowen, Orbit equivalence, coinduced actions and free products. Groups Geom. Dyn. 5 (2011), no. 1, pp. 1–15

DOI 10.4171/GGD/114