About relative polar varieties and Brasselet numbers

TL;DR

This paper investigates how the emptiness of relative polar varieties influences the topology of complex function-germs with potentially nonisolated singularities on singular varieties, providing new insights into their topological structure.

Contribution

It introduces new results linking the emptiness of relative polar varieties to the topology of nonisolated singularities in complex analytic spaces.

Findings

Empty polar varieties imply specific topological properties of the function-germ.

Results extend understanding of singularities beyond isolated cases.

Provides criteria for topological invariants based on polar variety conditions.

Abstract

In this work, we study the consequences of an empty polar variety on the topology of a function-germ with (possibly) nonisolated singularities defined on a singular variety.