Number of singularities of stable maps

Jorge T. Hiratuka, Osamu Saeki

Research output: Contribution to journalArticle

Abstract

We first derive a simple Euler characteristic formula for simplicial maps, based on their fibers. As applications, we give several formulas relating the Euler characteristics and the numbers of singularities of smooth generic maps in explicit situations, among which are singular surfaces in 3-dimensional manifolds, Morse functions on surfaces, stable maps of 4-dimensional manifolds into 3-dimensional manifolds, etc.

Original languageEnglish
Pages (from-to)53-69
Number of pages17
JournalJournal of Geometry
Volume89
Issue number1-2
DOIs
Publication statusPublished - Oct 1 2008

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Stable Map
Euler Characteristic
Singularity
Singular Surfaces
Morse Function
Fiber

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

Number of singularities of stable maps. / Hiratuka, Jorge T.; Saeki, Osamu.

In: Journal of Geometry, Vol. 89, No. 1-2, 01.10.2008, p. 53-69.

Research output: Contribution to journalArticle

Hiratuka, Jorge T. ; Saeki, Osamu. / Number of singularities of stable maps. In: Journal of Geometry. 2008 ; Vol. 89, No. 1-2. pp. 53-69.
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