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TOPOLOGY OF 1-PARAMETER DEFORMATIONS OF NON-ISOLATED REAL SINGULARITIES

Part of: Theory of singularities and catastrophe theory

Published online by Cambridge University Press:  30 July 2021

NICOLAS DUTERTRE  and
JUAN ANTONIO MOYA PÉREZ
NICOLAS DUTERTRE
Affiliation:
Univ Angers, CNRS, LAREMA, SFR MATHSTIC, F-49000 Angers, France. e-mail: nicolas.dutertre@univ-angers.fr
JUAN ANTONIO MOYA PÉREZ
Affiliation:
Departament de Matemàtiques, Universitat de València, Campus de Burjassot, 46100 Burjassot SPAIN e-mail: Juan.Moya@uv.es
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Abstract

Let $f\,{:}\,(\mathbb R^n,0)\to (\mathbb R,0)$ be an analytic function germ with non-isolated singularities and let $F\,{:}\, (\mathbb{R}^{1+n},0) \to (\mathbb{R},0)$ be a 1-parameter deformation of f. Let $ f_t ^{-1}(0) \cap B_\epsilon^n$ , $0 < \vert t \vert \ll \epsilon$ , be the “generalized” Milnor fiber of the deformation F. Under some conditions on F, we give a topological degree formula for the Euler characteristic of this fiber. This generalizes a result of Fukui.

MSC classification

Primary: 32B05: Analytic algebras and generalizations, preparation theorems
Secondary: 58K05: Critical points of functions and mappings 58K65: Topological invariants
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 2 , May 2022 , pp. 484 - 498
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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References

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