no. 1
Averages and the ℓ q,1 cohomology of Heisenberg groups
[Moyennes et cohomologie ℓ q,1 des groupes d’Heisenberg]
Pansu, Pierre1 ; Tripaldi, Francesca2
1 Laboratoire de Mathématiques d’Orsay Université Paris-Sud, CNRS Université Paris-Saclay 91405 Orsay FRANCE
2 Department of Mathematics and Statistics University of Jyväskylä 40014, Jyväskylä FINLAND
Annales mathématiques Blaise Pascal, Tome 26 (2019) no. 1, pp. 81-100.

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 :
DOI : 10.5802/ambp.384
Classification : 35R03, 58A10, 43A80
Keywords: Heisenberg groups, Rumin complex, $\ell ^{p}$ cohomology, parabolicity
Mot clés : Heisenberg groups, Rumin complex, $\ell ^{p}$ cohomology, parabolicity
Pansu, Pierre 1 ; Tripaldi, Francesca 2

1 Laboratoire de Mathématiques d’Orsay Université Paris-Sud, CNRS Université Paris-Saclay 91405 Orsay FRANCE
2 Department of Mathematics and Statistics University of Jyväskylä 40014, Jyväskylä FINLAND 
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     title = {Averages and the $\ell ^{q,1}$ cohomology of {Heisenberg} groups},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {81--100},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
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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. http://www.numdam.org/articles/10.5802/ambp.384/

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