Morse numbers of function germs with isolated singularities

TL;DR

This paper extends the classical Milnor number concept to holomorphic function germs with stratified isolated singularities, associating a set of Morse numbers that generalize the invariant to singular base spaces.

Contribution

It introduces a new set of Morse numbers for function germs with stratified isolated singularities, broadening the understanding of singularity invariants beyond smooth cases.

Findings

Defines Morse numbers for stratified singularities

Extends Milnor number concept to singular base spaces

Provides a framework for analyzing singularity invariants

Abstract

A set of Morse numbers is associated to a holomorphic function germ with stratified isolated singularity, extending the classical Milnor number to the setting of a singular base space.