Non-Orbit Equivalent Actions of $\Bbb F_n$

Details Non-Orbit Equivalent Actions of $\Bbb F_n$ Non-Orbit Equivalent Actions of $\Bbb F_n$

2006-10-16

arxiv.org/abs/math/0610452v2

Mathematics

Group Theory

final version

Scientific paper

For any $2\leq n\leq \infty$, we construct a concrete 1-parameter family of
non-orbit equivalent actions of the free group $\Bbb F_n$. These actions arise
as diagonal products between a generalized Bernoulli action and the action
$\Bbb F_n\curvearrowright (\Bbb T^2,\lambda^2)$, where $\Bbb F_n$ is seen as a
subgroup of SL$_2(\Bbb Z)$.

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