Fold maps with singular value sets of concentric spheres
Whitney and Thom started the study of fold maps, which are a generalization of Morse functions, in the 1950s. These maps were later studied in more generalization by many other mathematicians. In this article the author discusses a new kind of fold maps \(f: M \rightarrow \mathbb{R}^n\), called \textit{round fold maps}, by introducing two equivalent definitions of such maps. The author studies homotopy properties of manifolds admitting such maps and also the relationship between the homology of manifolds admitting round fold maps and that of the pre-image of the axis under these maps. Many examples are given for a better understanding of the concepts.
scientific article; zbMATH DE number 6383631