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

Abstract : 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.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-03310340
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Submitted on : Friday, February 25, 2022 - 2:25:27 PM
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OneParamDeforNonIsolated8.pdf
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### Citation

Nicolas Dutertre, Juan Antonio Moya Pérez. TOPOLOGY OF 1-PARAMETER DEFORMATIONS OF NON-ISOLATED REAL SINGULARITIES. Glasgow Mathematical Journal, Cambridge University Press (CUP), 2022, 64 (2), pp.484-498. ⟨10.1017/S0017089521000239⟩. ⟨hal-03310340⟩

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