2010/02/08 by Jean-Paul Brasselet, Jean‐Paul Brasselet, Brasselet, Jean-Paul +2
Mathematics · #32B20 #32B25 #58C35 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AP #math.DG #math.GT #msc:32B20 #msc:32B25 #msc:58C35
paper · pdf · doi:10.48550/arxiv.1002.1631
arxiv created 2010/02/08 · openalex publication_date 2010/02/08 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a real-analytic manifold and g\colon X→\mathbf Rn a proper triangulable subanalytic map. Given a subanalytic r-form ω on X whose pull-back to every non singular fiber of g is exact, we show tha ω has a relative primitive: there is a subanalytic (r-1)-form Ω such that dgΛ(ω-dΩ)=0. The proof uses a subanalytic triangulation to translate the problem in terms of "relative Whitney forms" associated to prisms. Using the combinatorics of Whitney forms, we show that the result ultimately follows from the subanaliticity of solutions of a special linear partial differential equation. The work was inspired by a question of François Treves.