Sobolev mappings and the spectral sequence for Rumin's filtration on the de Rham complex

2022/05/09 by Bruce Kleiner, Stefan C. Müller, Kleiner, Bruce +3 · 1 citation
Mathematics · #30C65 (Primary) #30L10 #53C17 (Secondary) #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.2205.04302

openalex publication_date 2022/05/09 · openalex created_date 2023/02/12 · openalex updated_date 2026/07/28

Abstract

We consider Rumin's filtration on the de Rham complex of a Carnot group. Although Pansu pullback by a Sobolev map is filtration preserving, it need not be a chain mapping. Nonetheless, we show that Pansu pullback induces a mapping of the associated spectral sequences. This gives an alternate interpretation of the Pullback Theorem from our previous paper.

Cited by

• Submanifolds with boundary in sub-Riemannian Heisenberg Groups

Related

• Sobolev mappings and the Rumin complex
• Multicomplexes on Carnot groups and their associated spectral sequence
• Pansu pullback and rigidity of mappings between Carnot groups
• Sobolev mappings between nonrigid Carnot groups
• Smooth contact lifts to central extensions of Carnot groups