On the topological triviality along moduli of deformations of $J_{k,0}$ singularities

Piotr Jaworski

ArticleOriginal scientific text

Title

On the topological triviality along moduli of deformations of $J_{k, 0}$ singularities

Authors ¹

Affiliations

Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Abstract

It is well known that versal deformations of nonsimple singularities depend on moduli. However they can be topologically trivial along some or all of them. The first step in the investigation of this phenomenon is to determine the versal discriminant (unstable locus), which roughly speaking is the obstacle to analytic triviality. The next one is to construct continuous liftable vector fields smooth far from the versal discriminant and to integrate them. In this paper we extend the results of J. Damon and A. Galligo, concerning the case of the Pham singularity (

J_{3, 0}

in Arnold's classification) (see [2, 3, 4]), and deal with deformations of general

J_{k, 0}

singularities.

Keywords

ENG

J_{k, 0}

singularities, topological trivialization, moduli of singularities

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Title

On the topological triviality along moduli of deformations of Jk,0 singularities

Affiliations

Abstract

Keywords

Bibliography

On the topological triviality along moduli of deformations of $J_{k, 0}$ singularities