On the Milnor fiber of a real map-germ.
type: Item
instance of: scholarly article
title: On the Milnor fiber of a real map-germ.
zbMATH Open document ID: 1081.14078
author: Nicolas Dutertre
published in: Hokkaido Mathematical Journal
publication date: 2002-01-01T00:00:00Z
review text: The Milnor fibre is a tool for the analysis of singularities of (real or complex) analytic map germs \(f:(\mathbb{K}^n,0)\to (\mathbb{K}^k,0)\). It is defined as \(\overline{B(0,\varepsilon)}\cap f^{-1}(y)\), where \(\overline{B(0,\varepsilon)}\) is a small closed ball and \(y\) is a small regular value of \(f\). The Milnor number is a numerical invariant associated with complex Milnor fibres. The author proves a real analogue of a formula about the Milnor number. It provides a connection between the Euler characteristics of two sets associated with the real Milnor fibre and a factor ring of the ring of germs of analytic functions. The Milnor number mod 2 of the complexification of the real map germ is known to be a topological invariant. A new and more elementary proof of this fact is presented.
reviewed by: Niels Schwartz
Mathematics Subject Classification ID: 14P15
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 32S55
zbMATH DE Number: 1809813
zbMATH Keywords: analytic map germs
zbMATH Keywords: singularities
zbMATH Keywords: complexification
zbMATH Keywords: Milnor number
zbMATH Keywords: Euler characteristic
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1350911866
OpenAlex ID: W2079739075
DOI: 10.14492/HOKMJ/1350911866
Recommended article: Q4224172
Recommended article: Topological invariants of real Milnor fibres
Recommended article: On the topology of the Milnor fibration
Recommended article: Topology of the real Milnor fiber for isolated singularities
Recommended article: Milnor fibers of real line arrangements
Recommended article: Real Milnor fibrations and \((C)\)-regularity
Recommended article: On the Euler characteristic of real Milnor fibres
Recommended article: Q4788736
Recommended article: ON THE CURVATURE OF THE REAL MILNOR FIBER
Recommended article: Q5755419
description: scientific article; zbMATH DE number 1809813