Averages and the $\ell ^{q,1}$ cohomology of Heisenberg groups

Pansu, Pierre; Tripaldi, Francesca

doi:10.5802/ambp.384

Averages and the

ℓ^{q, 1}

cohomology of Heisenberg groups
[Moyennes et cohomologie

ℓ^{q, 1}

des groupes d’Heisenberg]

Pierre Pansu ; Francesca Tripaldi

Annales Mathématiques Blaise Pascal, Tome 26 (2019) no. 1, pp. 81-100.

Résumé
Abstract

Les moyennes sont des invariants definis sur la cohomologie $ℓ^{1}$ des groupes de Lie. Nous démontrons que les moyennes dans les groupes abéliens et les groupes d’Heisenberg sont nulles. Ce résultat complète des travaux précédents et montre que la cohomologie $ℓ^{1}$ est nulle pour les groupes de Lie étudiés.

Averages are invariants defined on the $ℓ^{1}$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $ℓ^{1}$ cohomology vanishes in these cases.

Publié le : 2020-01-21

DOI : https://doi.org/10.5802/ambp.384
Classification : 35R03, 58A10, 43A80
Mots clés: Heisenberg groups, Rumin complex,

ℓ^{p}

cohomology, parabolicity

@article{AMBP_2019__26_1_81_0,
     author = {Pierre Pansu and Francesca Tripaldi},
     title = {Averages and the $\ell ^{q,1}$ cohomology of Heisenberg groups},
     journal = {Annales Math\'ematiques Blaise Pascal},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {26},
     number = {1},
     year = {2019},
     pages = {81-100},
     doi = {10.5802/ambp.384},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2019__26_1_81_0/}
}

Pansu, Pierre; Tripaldi, Francesca. Averages and the $\ell ^{q,1}$ cohomology of Heisenberg groups. Annales Mathématiques Blaise Pascal, Tome 26 (2019) no. 1, pp. 81-100. doi : 10.5802/ambp.384. https://ambp.centre-mersenne.org/item/AMBP_2019__26_1_81_0/

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