A note on nonremovable cusp singularities
type: Item
instance of: scholarly article
title: A note on nonremovable cusp singularities
zbMATH Open document ID: 1006.57011
author: Kazuhiro Sakuma
published in: Hiroshima Mathematical Journal
publication date: 2003-03-04T00:00:00Z
review text: Let \(f:M^4\to N^3\) be a smooth map. The author proves that if \(N^3\) is an orientable 3-manifold and \(M^4\) is a closed orientable 4-manifold such that \(\text{rank}_\mathbb{Z} H_2(M^4, \mathbb{Z}_2)=1\), then there does not exist a smooth map \(f:M^4\to N^3\) with only fold singularities. As a consequence he proves that every stable map \(f:M^4\to N^3\) always has cusp singularities, although the Thom polynomial of cusp singularities of \(f\) always vanishes.
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 57R42
zbMATH DE Number: 1741728
zbMATH Keywords: stable map
zbMATH Keywords: Thom polynomial
reviewed by: Stanisław Janeczko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1151105733
OpenAlex ID: W2150581741
Wikidata QID: Q128869897
DOI: 10.32917/HMJ/1151105733
description: scientific article; zbMATH DE number 1741728