Isotopy of Morin singularities

Abstract

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

Criteria for Morin singularities for maps into lower dimensions, and applications

“…Using them, we give applications to bifurcation of the Lefschetz singularity which plays important roles in low-dimensional topology. See [5,6,10,21,22,23,24,29,30] for other investigations of Morin singularities.…”