Desingularizing special generic maps into 3-dimensional space

TL;DR

This paper investigates conditions under which special generic maps from higher-dimensional manifolds into 3D space can be decomposed into simpler components, enhancing understanding of their structure and classification.

Contribution

It provides new criteria for factoring special generic maps into embeddings and projections in specific dimension settings, advancing the theory of singular maps.

Findings

Established conditions for factorization of special generic maps into 3D

Extended understanding of the structure of special generic maps

Contributed to the classification of singular maps in differential topology

Abstract

A smooth map between smooth manifolds is called a special generic map if it has only definite fold points as its singularities. In this paper, we give conditions for a special generic map into the 3-dimensional Euclidean space to be factored as the composition of an embedding and a projection for certain dimensions.