2001/11/13 by Raffaele Vitolo, R. Vitolo, Vitolo, R.
Mathematics · Physics and Astronomy · #58A12 #58A20 #58E99 #58J10 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math-ph #math.AP #math.DG #math.MP #msc:58A12 #msc:58A20 #msc:58E99 #msc:58J10
paper · pdf · doi:10.48550/arxiv.math/0111161
LaTeX2e, amslatex, diagrams, hyperref; 23 p. To appear in Acta Applicandae Mathematicae
arxiv created 2001/11/13 · openalex publication_date 2001/11/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The C-spectral sequence was introduced by Vinogradov in the late Seventies as a fundamental tool for the study of algebro-geometric properties of jet spaces and differential equations. A spectral sequence arise from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation). In order to avoid serious technical difficulties, the order of the jet space is not fixed, i. e., computations are performed on spaces containing forms on jet spaces of any order. In this paper we show that there exists a formulation of Vinogradov's C-spectral sequence in the case of finite order jet spaces of a fibred manifold. We compute all cohomology groups of the finite order C-spectral sequence. We obtain a finite order variational sequence which is shown to be naturally isomorphic with Krupka's finite order variational sequence.