Sufficiency of non-isolated singularities

TL;DR

This paper establishes a sufficient condition based on the Łojasiewicz inequality for $C^k$-mapping germs with non-isolated singularities at zero to be isotopical, advancing understanding of singularity behavior.

Contribution

It introduces a new criterion using the Łojasiewicz inequality to determine isotopical equivalence of non-isolated singularities in $C^k$-mappings.

Findings

Provides a sufficient condition for isotopicality

Uses Łojasiewicz inequality as a key tool

Enhances classification of non-isolated singularities

Abstract

We give, in terms of the {\L}ojasiewicz inequality, a sufficient condition for $C^k$-mappings germs of non-isolated singularity at zero to be isotopical.