Isotopy of Morin singularities

TL;DR

This paper introduces A-isotopy, a strengthened equivalence relation for finitely determined map-germs, and explores the classification of Morin singularities and their stable perturbations.

Contribution

It defines A-isotopy for map-germs, analyzes A-isotopy classes of Morin singularities, and applies these concepts to stable perturbations of simple equi-dimensional map-germs.

Findings

Number of A-isotopy classes for Morin singularities analyzed

Classification results for low-dimensional singularities provided

Application to stable perturbations of simple map-germs included

Abstract

We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable perturbations of simple equi-dimensional map-germs.