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VOL. 66 | 2015 Survey of apparent contours of stable maps between surfaces
Takahiro Yamamoto

Editor(s) Vincent Blanlœil, Osamu Saeki

Abstract

This is a survey paper about studies of the simplest shape of the apparent contour for stable maps between surfaces. Such studies first appeared in [10] then in [1], [3], [6], [20], [22]. Let $M$ be a connected and closed surface, $N$ a connected surface. For a stable map $\varphi: M\to N$, denote by $c(\varphi)$, $n(\varphi)$ and $i(\varphi)$ the numbers of cusps, nodes and singular set components of $\varphi$, respectively. For a $C^\infty$ map $\varphi_0 : M\to S^2$ into the sphere, we study the minimal pair $(i, c+n)$ and triples $(i,c,n)$, $(c,i,n)$, $(n,c,i)$ and $(i,n,c)$ among stable maps $M\to S^2$ homotopic to $\varphi_0$ with respect to the lexicographic order.

Information

Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1360.57037
MathSciNet: MR3382040

Digital Object Identifier: 10.2969/aspm/06610013

Subjects:
Primary: 57R45
Secondary: 57R35, 58K15

Keywords: cusp, Node, stable map

Rights: Copyright © 2015 Mathematical Society of Japan

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