The minimal number of singularities of stable maps between surfaces
type: Item
instance of: scholarly article
title: The minimal number of singularities of stable maps between surfaces
zbMATH Open document ID: 1207.57039
author: Atsushi Kamenosono
author: Takahiro Yamamoto
published in: Topology and its Applications
publication date: 2009-08-20T00:00:00Z
review text: For a stable smooth map \(f\) of degree \(d\) of a closed connected surface into the sphere, let \(c, i\), and \(n\) denote the number of cusps, fold-curve components, and nodes, respectively. The main result of the paper is the determination of the minimal pair \((i,c+n)\) with respect to the lexicographic order. On the one hand, the proof relies on Euler-characteristic analysis, and on the other hand, on constructing maps with desired properties (with gluing techniques).
reviewed by: Richárd Rimányi
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 5597517
zbMATH Keywords: singularities
zbMATH Keywords: stable maps
MaRDI profile type: Publication
full work available at URL: j.topol.2009.06.010
OpenAlex ID: W2046644474
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DOI: 10.1016/J.TOPOL.2009.06.010
description: scientific article; zbMATH DE number 5597517