2019/05/30 by A. Lesfari, Lesfari, A.
Mathematics · #32C35 #53D05 #58A10 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Functional Equations Stability Results #General Mathematics (math.GM) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1905.13347
openalex publication_date 2019/05/30 · openalex created_date 2019/06/07 · openalex updated_date 2026/07/28
The Poincaré lemma (or Volterra theorem) is of utmost importance both in theory and in practice. It tells us every differential form which is closed, is locally exact. In other words, on a contractible manifold all closed forms are exact. The aim of this paper is to present some direct proofs of this lemma and explore some of its numerous consequences. Some connections with Cech-De Rham-Dolbeault cohomologies, ∂-Poincaré lemma or Dolbeault-Grothendieck lemma are given.