Analytic properties of approximate lattices  [ Propriétés analytiques de réseaux approximatifs ]
Annales de l'Institut Fourier, à paraître, 48 p.

Nous introduisons une notion d’induction de cocycle pour les réseaux approximatifs uniformes forts dans les groupes localement compacts à base dénombrable, et nous l’utilisons pour mettre en relation les réseaux approximatifs de type Kazhdan et Haagerup (relatifs) avec les propriétés correspondantes des groupes ambiants localement compacts. Notre approche s’applique à de larges classes de réseaux approximatifs uniformes (bien que pas toutes) et est suffisamment souple pour couvrir les versions L p de propriété (FH) et a-(FH)-moyennabilité, ainsi que leurs versions quasi à la Burger–Monod et Ozawa.

We introduce a notion of cocycle-induction for strong uniform approximate lattices in locally compact second countable groups and use it to relate (relative) Kazhdan- and Haagerup-type of approximate lattices to the corresponding properties of the ambient locally compact groups. Our approach applies to large classes of uniform approximate lattices (though not all of them) and is flexible enough to cover the L p -versions of Property (FH) and a-(FH)-menability as well as quasified versions thereof a la Burger–Monod and Ozawa.

Reçu le : 2017-10-13
Révisé le : 2018-09-27
Accepté le : 2019-05-21
Première publication : 2020-10-01
Classification : 20N99,  22D10,  22E40
Mots clés: Réseaux approximatifs, propriété (T), propriét é (FH), propriété Haagerup 
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     author = {Bj\"orklund, Michael and Hartnick, Tobias},
     title = {Analytic properties of approximate lattices},
     note = {to appear in \emph{Annales de l'Institut Fourier}},
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Björklund, Michael; Hartnick, Tobias. Analytic properties of approximate lattices. Annales de l'Institut Fourier, à paraître, 48 p.

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