- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:59
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
5
2011
1
Orbit equivalence, coinduced actions and free products
Lewis
Bowen
The University of Texas at Austin, AUSTIN, UNITED STATES
Coinduced, orbit equivalence, Bernoulli shifts
The following result is proven. Let $G_1 \curvearrowright^{T_1} (X_1,\mu_1)$ and $G_2 \curvearrowright^{T_2} (X_2,\mu_2)$ be orbit equivalent (OE), essentially free, probability measure preserving actions of countable groups $G_1$ and $G_2$. Let $H$ be any countable group. For $i=1,2$, let $\Gamma_i = G_i *H$ be the free product. Then the actions of $\Gamma_1$ and $\Gamma_2$ coinduced from $T_1$ and $T_2$ are OE. As an application, it is shown that if $\Gamma$ is a free group, then all nontrivial Bernoulli shifts over $\Gamma$ are OE.
Dynamical systems and ergodic theory
General
1
15
10.4171/GGD/114
http://www.ems-ph.org/doi/10.4171/GGD/114