An alternative proof of a formula on Euler characteristics of singularity sets of a Morin map \(M \rightarrow \mathbb{R}^n\) based on Morse theory
type: Item
instance of: scholarly article
title: An alternative proof of a formula on Euler characteristics of singularity sets of a Morin map \(M \rightarrow \mathbb{R}^n\) based on Morse theory
zbMATH Open document ID: 1394.57026
author: Camila M. Ruiz
published in: Topology and its Applications
publication date: 2018-01-05T00:00:00Z
review text: For a Morin map \(f:M\to N\), where \(M\) is a compact and \(N\) a connected manifold, \textit{N. Dutertre} and \textit{T. Fukui} established a formula (Theorem 6.2 of [J. Math. Soc. Japan 66, No. 1, 161--203 (2014; Zbl 1294.57018)]) relating the Euler characteristic of \(M\) and the Euler characteristic of the singular sets of \(f\). The present paper gives a new proof of this result in the special case \(N=\mathbb{R}^n\) using Morse theory on manifolds with boundary.
reviewed by: Thomas J. Bartsch
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 57R70
zbMATH DE Number: 6822544
zbMATH Keywords: Morin singularities
zbMATH Keywords: Morse theory
zbMATH Keywords: Euler characteristic
MaRDI profile type: Publication
full work available at URL: j.topol.2017.11.012
OpenAlex ID: W2770921093
cites work: On the topology of stable maps
cites work: Q3806393
cites work: Studying the topology of Morin singularities from a global viewpoint
cites work: Nondegenerate critical manifolds
cites work: Un théorème de Zariski du type de Lefschetz
cites work: ON TOPOLOGICAL INVARIANTS ASSOCIATED WITH A POLYNOMIAL WITH ISOLATED CRITICAL POINTS
DOI: 10.1016/J.TOPOL.2017.11.012
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description: scientific article; zbMATH DE number 6822544