L\^e-Greuel type formula for the Euler obstruction and applications

TL;DR

This paper extends the Lê-Greuel formula to the Euler obstruction of functions on singular spaces, providing new integral formulas and generalizations that deepen understanding of singularity invariants.

Contribution

It introduces a Lê-Greuel type formula for the Euler obstruction of functions on singular spaces and generalizes existing integral formulas for this invariant.

Findings

Derived a Lê-Greuel type formula for Euler obstruction

Presented an integral formula for the Euler obstruction of a function

Generalized Kennedy's formula using results of Loeser

Abstract

The Euler obstruction of a function can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we give a version of the L\^e-Greuel formula for two germs of analytic functions with isolated singularity at the origin on a singular space. Using this formula and results of Loeser, we also present an integral formula for the Euler obstruction of a function, generalizing a formula of Kennedy.