De Rham theorem for Whitney functions

TL;DR

This paper proves that on a real analytic manifold, the Whitney-de Rham complex associated with a constructible sheaf is quasi-isomorphic to the sheaf itself, establishing a de Rham-type theorem.

Contribution

It establishes a De Rham theorem for Whitney functions, linking Whitney-de Rham complexes to constructible sheaves on real analytic manifolds.

Findings

Whitney-de Rham complex is quasi-isomorphic to the constructible sheaf

Provides a De Rham theorem in the context of Whitney functions

Extends classical De Rham results to real analytic manifolds with constructible sheaves

Abstract

Let M be a real analytic manifold, F a bounded complex of constructible sheaves. We show that the Whitney-de Rham complex associated to F is quasi-isomorphic to F.