TOPOLOGY OF 1-PARAMETER DEFORMATIONS OF NON-ISOLATED REAL SINGULARITIES
Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 484-498
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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.
DUTERTRE, NICOLAS; PÉREZ, JUAN ANTONIO MOYA. TOPOLOGY OF 1-PARAMETER DEFORMATIONS OF NON-ISOLATED REAL SINGULARITIES. Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 484-498. doi: 10.1017/S0017089521000239
@article{10_1017_S0017089521000239,
author = {DUTERTRE, NICOLAS and P\'EREZ, JUAN ANTONIO MOYA},
title = {TOPOLOGY {OF} {1-PARAMETER} {DEFORMATIONS} {OF} {NON-ISOLATED} {REAL} {SINGULARITIES}},
journal = {Glasgow mathematical journal},
pages = {484--498},
year = {2022},
volume = {64},
number = {2},
doi = {10.1017/S0017089521000239},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000239/}
}
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