Cocycle and orbit equivalence superrigidityfor malleable actions of w-rigid groups
Identifieur interne : 000A33 ( Main/Merge ); précédent : 000A32; suivant : 000A34Cocycle and orbit equivalence superrigidityfor malleable actions of w-rigid groups
Auteurs : Sorin Popa [États-Unis]Source :
- Inventiones mathematicae [ 0020-9910 ] ; 2007-11-01.
Abstract
Abstract: We prove that if a countable discrete group Γ is w-rigid, i.e. it contains an infinite normal subgroup H with the relative property (T) (e.g. $\Gamma=SL(2,\mathbb{Z})\ltimes\mathbb{Z}^2$ , or Γ=H×H’ with H an infinite Kazhdan group and H’ arbitrary), and $\mathcal{V}$ is a closed subgroup of the group of unitaries of a finite separable von Neumann algebra (e.g. $\mathcal{V}$ countable discrete, or separable compact), then any $\mathcal{V}$ -valued measurable cocycle for a measure preserving action $\Gamma\curvearrowright X$ of Γ on a probability space (X,μ) which is weak mixing on H and s-malleable (e.g. the Bernoulli action $\Gamma\curvearrowright[0,1]^{\Gamma}$ ) is cohomologous to a group morphism of Γ into $\mathcal{V}$ . We use the case $\mathcal{V}$ discrete of this result to prove that if in addition Γ has no non-trivial finite normal subgroups then any orbit equivalence between $\Gamma\curvearrowright X$ and a free ergodic measure preserving action of a countable group Λ is implemented by a conjugacy of the actions, with respect to some group isomorphism Γ≃Λ.
Url:
DOI: 10.1007/s00222-007-0063-0
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 000B62
- to stream Istex, to step Curation: 000B62
- to stream Istex, to step Checkpoint: 000973
Links to Exploration step
ISTEX:386065F4A008AC57F5C23D7F12C7728CA15E0BF5Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Cocycle and orbit equivalence superrigidityfor malleable actions of w-rigid groups</title><author><name sortKey="Popa, Sorin" sort="Popa, Sorin" uniqKey="Popa S" first="Sorin" last="Popa">Sorin Popa</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:386065F4A008AC57F5C23D7F12C7728CA15E0BF5</idno><date when="2007" year="2007">2007</date><idno type="doi">10.1007/s00222-007-0063-0</idno><idno type="url">https://api.istex.fr/document/386065F4A008AC57F5C23D7F12C7728CA15E0BF5/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000B62</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000B62</idno><idno type="wicri:Area/Istex/Curation">000B62</idno><idno type="wicri:Area/Istex/Checkpoint">000973</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000973</idno><idno type="wicri:doubleKey">0020-9910:2007:Popa S:cocycle:and:orbit</idno><idno type="wicri:Area/Main/Merge">000A33</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Cocycle and orbit equivalence superrigidityfor malleable actions of w-rigid groups</title><author><name sortKey="Popa, Sorin" sort="Popa, Sorin" uniqKey="Popa S" first="Sorin" last="Popa">Sorin Popa</name><affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Math.Dept., UCLA, University of California, 90095-155505, Los Angeles, CA</wicri:regionArea><placeName><region type="state">Californie</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Inventiones mathematicae</title><title level="j" type="abbrev">Invent. math.</title><idno type="ISSN">0020-9910</idno><idno type="eISSN">1432-1297</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>Berlin/Heidelberg</pubPlace><date type="published" when="2007-11-01">2007-11-01</date><biblScope unit="volume">170</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="243">243</biblScope><biblScope unit="page" to="295">295</biblScope></imprint><idno type="ISSN">0020-9910</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0020-9910</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We prove that if a countable discrete group Γ is w-rigid, i.e. it contains an infinite normal subgroup H with the relative property (T) (e.g. $\Gamma=SL(2,\mathbb{Z})\ltimes\mathbb{Z}^2$ , or Γ=H×H’ with H an infinite Kazhdan group and H’ arbitrary), and $\mathcal{V}$ is a closed subgroup of the group of unitaries of a finite separable von Neumann algebra (e.g. $\mathcal{V}$ countable discrete, or separable compact), then any $\mathcal{V}$ -valued measurable cocycle for a measure preserving action $\Gamma\curvearrowright X$ of Γ on a probability space (X,μ) which is weak mixing on H and s-malleable (e.g. the Bernoulli action $\Gamma\curvearrowright[0,1]^{\Gamma}$ ) is cohomologous to a group morphism of Γ into $\mathcal{V}$ . We use the case $\mathcal{V}$ discrete of this result to prove that if in addition Γ has no non-trivial finite normal subgroups then any orbit equivalence between $\Gamma\curvearrowright X$ and a free ergodic measure preserving action of a countable group Λ is implemented by a conjugacy of the actions, with respect to some group isomorphism Γ≃Λ.</div></front></TEI></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Merge
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000A33 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Merge/biblio.hfd -nk 000A33 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Main
|étape= Merge
|type= RBID
|clé= ISTEX:386065F4A008AC57F5C23D7F12C7728CA15E0BF5
|texte= Cocycle and orbit equivalence superrigidityfor malleable actions of w-rigid groups
}}
| This area was generated with Dilib version V0.6.33. |  |