Journal article
Orbit Equivalence Rigidity for Product Actions
Communications in mathematical physics, Vol.379(1), pp.41-59
10/01/2020
DOI: 10.1007/s00220-019-03598-y
Abstract
Let
Γ
1
,
⋯
,
Γ
n
be hyperbolic, property (T) groups, for some
n
≥
1
. We prove that if a product
Γ
1
×
⋯
×
Γ
n
↷
X
1
×
⋯
×
X
n
of measure preserving actions is stably orbit equivalent to a measure preserving action
Λ
↷
Y
, then
Λ
↷
Y
is induced from an action
Λ
0
↷
Y
0
such that there exists a direct product decomposition
Λ
0
=
Λ
1
×
⋯
×
Λ
n
into
n
infinite groups. Moreover, there exists a measure preserving action
Λ
i
↷
Y
i
that is stably orbit equivalent to
Γ
i
↷
X
i
, for any
1
≤
i
≤
n
, and the product action
Λ
1
×
⋯
×
Λ
n
↷
Y
1
×
⋯
×
Y
n
is isomorphic to
Λ
0
↷
Y
0
.
Details
- Title: Subtitle
- Orbit Equivalence Rigidity for Product Actions
- Creators
- Daniel Drimbe - University of Regina
- Resource Type
- Journal article
- Publication Details
- Communications in mathematical physics, Vol.379(1), pp.41-59
- DOI
- 10.1007/s00220-019-03598-y
- ISSN
- 0010-3616
- eISSN
- 1432-0916
- Publisher
- Springer Berlin Heidelberg
- Grant note
- Pacific Institute for the Mathematical Sciences (http://dx.doi.org/10.13039/100009059)
- Language
- English
- Date published
- 10/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984696654902771
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