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

2019/04/14 by Pierre Pansu, Pansu, Pierre, Francesca Tripaldi +1
Mathematics · #35R03 (Primary) #43A80 (Secondary) #58A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1904.06669

openalex publication_date 2019/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Averages are invariants defined on the ℓ¹ 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 ℓ¹ cohomology vanishes in these cases.

Citations

• Poincaré and Sobolev inequalities for differential forms in Heisenberg groups

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