Averages and the q,1 cohomology of Heisenberg groups
Annales mathématiques Blaise Pascal, Volume 26 (2019) no. 1, pp. 81-100.

Averages are invariants defined on the 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 1 cohomology vanishes in these cases.

Les moyennes sont des invariants definis sur la cohomologie 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 1 est nulle pour les groupes de Lie étudiés.

Published online:
DOI: 10.5802/ambp.384
Classification: 35R03,  58A10,  43A80
Keywords: Heisenberg groups, Rumin complex, p cohomology, parabolicity
Pierre Pansu 1; Francesca Tripaldi 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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Pierre Pansu; Francesca Tripaldi. Averages and the $\ell ^{q,1}$ cohomology of Heisenberg groups. Annales mathématiques Blaise Pascal, Volume 26 (2019) no. 1, pp. 81-100. doi : 10.5802/ambp.384. https://ambp.centre-mersenne.org/articles/10.5802/ambp.384/

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