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

Abstract

Averages are invariants defined on the ${\ell }^1$ 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 ${\ell }^1$ cohomology vanishes in these cases.

References in corpus (2)

• Poincar{é} and Sobolev inequalities for differential forms in Heisenberg groups
• $L^1$-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups