A Poincaré lemma for Whitney–de Rham complex

Abstract

Let M be a real analytic manifold, Z a closed subanalytic subset of M . We show that the Whitney-de Rham complex over Z is quasi-isomorphic to the constant sheaf C Z .

De Rham theorem for Whitney functions

“…As a corollary we obtain a theorem of [4]. (Another proof was given in [5] using deep results on D-modules. ) We also obtain a de Rham theorem for Schwartz functions on open subanalytic subsets.…”