Fold maps with singular value sets of concentric spheres
type: Item
instance of: scholarly article
title: Fold maps with singular value sets of concentric spheres
zbMATH Open document ID: 1307.57018
author: Naoki Kitazawa
published in: Hokkaido Mathematical Journal
publication date: 2015-01-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.hokmj/1416837569
review text: 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.
reviewed by: Keerti Vardhan
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 57N15
zbMATH DE Number: 6383631
zbMATH Keywords: singularities of differentiable maps
zbMATH Keywords: singular sets
zbMATH Keywords: fold maps
zbMATH Keywords: round fold maps
zbMATH Keywords: differential topology
MaRDI profile type: Publication
OpenAlex ID: W1992959165
DOI: 10.14492/HOKMJ/1416837569
description: scientific article; zbMATH DE number 6383631