Averages and the l^q,1-cohomology of Heisenberg groups

Pierre Pansu (1) , Francesca Tripaldi (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 JYU - Department of Mathematics and Statistics [Jyväskylä Univ]

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.

Mots clés: Heisenberg groups; Rumin complex; l^p cohomology; parabolicity

Domaines: Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]; Théorie des groupes [math.GR]

Pierre Pansu, Francesca Tripaldi. Averages and the l^q,1-cohomology of Heisenberg groups. 2019. ⟨hal-02098935⟩