Singularities and stable homotopy groups of spheres I

TL;DR

This paper explores the relationship between Morin singularities and stable homotopy groups of spheres, using this connection to compute cobordism groups of singular maps via spectral sequences.

Contribution

It introduces a novel link between singularity theory and stable homotopy groups, enabling new computations of cobordism groups of singular maps.

Findings

Differentials in the spectral sequence are given by composition multiplication in stable homotopy groups.

Established a method to compute cobordism groups of certain singular maps.

Connected Morin singularities with stable homotopy groups of spheres.

Abstract

We establish an interesting connection between Morin singularities and stable homotopy groups of spheres. We apply this connection to computations of cobordism groups of certain singular maps. The differentials of the spectral sequence computing these cobordism groups are given by the composition multiplication in the stable homotopy groups of spheres.