Non-orbit equivalent actions of 𝔽 n

Adrian Ioana

Annales scientifiques de l'École Normale Supérieure (2009)

  • Volume: 42, Issue: 4, page 675-696
  • ISSN: 0012-9593

Abstract

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For any 2 ≤ n ≤ ∞ , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group 𝔽 n . These actions arise as diagonal products between a generalized Bernoulli action and the action 𝔽 n ↷ ( 𝕋 2 , λ 2 ) , where 𝔽 n is seen as a subgroup of SL 2 ( ℤ ) .

How to cite

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Ioana, Adrian. "Non-orbit equivalent actions of $\mathbb {F}_n$." Annales scientifiques de l'École Normale Supérieure 42.4 (2009): 675-696. <http://eudml.org/doc/272249>.

@article{Ioana2009,
abstract = {For any $2\le n\le \infty $, we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group $\mathbb \{F\}_n$. These actions arise as diagonal products between a generalized Bernoulli action and the action $\mathbb \{F\}_n\curvearrowright (\mathbb \{T\}^2,\lambda ^2)$, where $\mathbb \{F\}_n$ is seen as a subgroup of $\mathrm \{SL\}_2(\mathbb \{Z\})$.},
author = {Ioana, Adrian},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {free groups; orbit equivalence},
language = {eng},
number = {4},
pages = {675-696},
publisher = {Société mathématique de France},
title = {Non-orbit equivalent actions of $\mathbb \{F\}_n$},
url = {http://eudml.org/doc/272249},
volume = {42},
year = {2009},
}

TY - JOUR
AU - Ioana, Adrian
TI - Non-orbit equivalent actions of $\mathbb {F}_n$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2009
PB - Société mathématique de France
VL - 42
IS - 4
SP - 675
EP - 696
AB - For any $2\le n\le \infty $, we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group $\mathbb {F}_n$. These actions arise as diagonal products between a generalized Bernoulli action and the action $\mathbb {F}_n\curvearrowright (\mathbb {T}^2,\lambda ^2)$, where $\mathbb {F}_n$ is seen as a subgroup of $\mathrm {SL}_2(\mathbb {Z})$.
LA - eng
KW - free groups; orbit equivalence
UR - http://eudml.org/doc/272249
ER -

References

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