The Rumin complex on nilpotent Lie groups

2020/09/21 by Francesca Tripaldi, Tripaldi, Francesca
Mathematics · #22E25 #57R19 #58A15 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:22E25 #msc:57R19 #msc:58A15

paper · pdf · doi:10.48550/arxiv.2009.10154

arxiv created 2020/09/21 · openalex publication_date 2020/09/21 · arxiv updated 2020/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper an alternative definition of the Rumin complex (E₀^\bullet,d_c) is presented, one that relies on a different concept of weights of forms. In this way, the Rumin complex can be constructed on any nilpotent Lie group equipped with a Carnot-Carathéodory metric. Moreover, this construction allows for the direct application of previous non-vanishing results of ℓ^q,p cohomology to all nilpotent Lie groups that admit a positive grading.

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