A Poincar\'{e} Lemma for Whitney-de Rham complex

TL;DR

This paper proves that the Whitney-de Rham complex over a closed subanalytic subset of a real analytic manifold is quasi-isomorphic to the constant sheaf, establishing a Poincaré lemma in this context.

Contribution

It introduces a Poincaré lemma for the Whitney-de Rham complex on subanalytic subsets, linking it to the constant sheaf in a new setting.

Findings

Whitney-de Rham complex over Z is quasi-isomorphic to the constant sheaf.

Establishes a Poincaré lemma for Whitney-de Rham complex on subanalytic sets.

Provides a new tool for analyzing sheaf complexes on subanalytic subsets.

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 $\mathbb{C}_{Z}$