Round fold maps of n--dimensional manifolds into ${\mathbb{R}}^{n-1}$

Abstract

We determine those smooth $n$--dimensional closed manifolds with $n\ge 4$ which admit round fold maps into ${\mathbb{R}}^{n-1}$, i.e.\ fold maps whose critical value sets consist of disjoint spheres of dimension $n-2$ isotopic to concentric spheres. We also classify such round fold maps up to $C^{\infty }$ $\mathcal{A}$--equivalence.

12 pages, 1 figure. arXiv admin note: text overlap with arXiv:2105.00974