Invariants of Topological Relative Right Equivalences
Imran Ahmed, Maria Aparecida Soares Ruas, Jo\~ao Nivaldo Tomazella
TL;DR
This paper investigates the invariants of topological relative right equivalences, focusing on the constancy of the Milnor number in families of functions with isolated singularities on analytic varieties.
Contribution
It extends the understanding of Milnor number invariance to families of functions on analytic varieties, providing new characterizations in the relative setting.
Findings
Milnor number remains constant under certain topological equivalences
Characterizations of invariance are adapted to functions on analytic varieties
Provides a framework for analyzing singularities in a relative context
Abstract
The constancy of the Milnor number has several characterizations which were summarized by Greuel in 1986. This paper presents a study of these characterizations in the case of families of functions with isolated singularities defined on an analytic variety.
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