$L^\infty$ cohomology is intersection cohomology

TL;DR

This paper establishes a De Rham theorem linking $L^ Infty$ forms to intersection cohomology on subanalytic compact pseudomanifolds, demonstrating an isomorphism in the maximal perversity case.

Contribution

It proves that the cohomology of $L^ Infty$ forms is isomorphic to intersection cohomology, providing a new analytic approach to understanding intersection cohomology.

Findings

Cohomology of $L^ Infty$ forms is isomorphic to intersection cohomology.

De Rham theorem extended to $L^ Infty$ forms on pseudomanifolds.

Isomorphism holds in the maximal perversity case.

Abstract

Let $X$ be any subanalytic compact pseudomanifold. We show a De Rham theorem for $L^\infty$ forms. We prove that the cohomology of $L^\infty$ forms is isomorphic to intersection cohomology in the maximal perversity.