Categorical Properties Of Smooth Unfoldings On Stratified Spaces

TL;DR

This paper extends the theory of unfoldings in stratified spaces by introducing unbendings, providing a new approach to desingularization that generalizes previous results for Thom-Mather spaces.

Contribution

It introduces unbendings as a new class of desingularizations, generalizing primary unfoldings to stratified pseudomanifolds of arbitrary finite length.

Findings

Unbendings coincide with primary unfoldings in simple cases

Extended the uniqueness and functoriality results to more complex stratified spaces

Provided a new framework for desingularization of stratified pseudomanifolds

Abstract

In a previous work we proved the uniqueness and functoriality of primary unfoldings on simple Thom-Mather spaces, which is a functor to the category of smooth manifolds. In this article we extend these results for any stratified Thom-Mather pseudomanifold with arbitary finite length, through a new kind of intermediate desingularizations, the unbendings, which coincide with primary unfoldings in the simple case.