On asymptotic and continuous group Orlicz cohomology
[Sur la cohomologie d’Orlicz asymptotique et continue des groupes]
Annales de l'Institut Fourier, Online first, 44 p.

On généralise quelques résultats sur la cohomologie L p asymptotique et continue des groupes à la cohomologie d’Orlicz. En particulier, on montre que la cohomologie d’Orlicz asymptotique est invariante sous quasi-isométries et que les deux notions coïncident dans le cas des groupes localement compacts à base dénombrable d’ouverts. Le cas de degré 1 est étudié plus en détail.

We generalize some results on asymptotic and continuous group L p -cohomology to Orlicz cohomology. In particular, we show that asymptotic Orlicz cohomology is a quasi-isometry invariant and that both notions coincide in the case of a locally compact second countable group. The case of degree 1 is studied in more detail.

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DOI : 10.5802/aif.3704
Classification : 20J06, 46E30, 51F30
Keywords: Orlicz cohomology, quasi-isometry invariance, topological group
Mots-clés : Cohomologie d’Orlicz, invariance sous quasi-isométies, groupe topologique

Kopylov, Yaroslav 1 ; Sequeira, Emiliano 2

1 Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., Novosibirsk 630090 (Russia)
2 Centro de Matemática, FCIEN-Universidad de la República, 4225 Igua, Montevideo 11400 (Uruguay)
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Kopylov, Yaroslav; Sequeira, Emiliano. On asymptotic and continuous group Orlicz cohomology. Annales de l'Institut Fourier, Online first, 44 p.

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