no. 5
On asymptotic and continuous group Orlicz cohomology
Kopylov, Yaroslav1; Sequeira, Emiliano2
1Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., Novosibirsk 630090 (Russia)
2Centro de Matemática, FCIEN-Universidad de la República, 4225 Igua, Montevideo 11400 (Uruguay)
Annales de l'Institut Fourier, Volume 75 (2025) no. 5, pp. 1855-1898

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.

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.

Received:
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Accepted:
Online First:
Published online:
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)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Kopylov, Yaroslav; Sequeira, Emiliano. On asymptotic and continuous group Orlicz cohomology. Annales de l'Institut Fourier, Volume 75 (2025) no. 5, pp. 1855-1898. doi: 10.5802/aif.3704

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