On The Functorialrily Of Stratified Desingularizations

TL;DR

This paper investigates the functorial properties of stratified desingularizations within Thom-Mather simple spaces, establishing a unique primary unfolding for each space that aids in defining De Rham Intersection Cohomology.

Contribution

It constructs a functorial primary unfolding for Thom-Mather simple spaces and proves its uniqueness up to Thom-Mather isomorphisms, advancing the understanding of desingularization processes.

Findings

Primary unfoldings are functorial for Thom-Mather simple spaces.

Uniqueness of primary unfoldings up to Thom-Mather isomorphisms.

Facilitates the use of smooth desingularizations in De Rham Intersection Cohomology.

Abstract

This article is devoted to the study of smooth desingularization, which are customary employed in the definition of De Rham Intersection Cohomology with differential forms. In this paper we work with the category of Thom-Mather simple spaces. We construct a functor which sends each Thom-Mather simple space into a smooth manifold called its primary unfolding. Hence we prove that the primary unfoldings are unique up Thom-Mather isomorphisms.