Milnor fibrations of meromorphic functions

TL;DR

This paper explores the topological properties of Milnor fibrations associated with meromorphic functions, comparing local fibrations near critical values with global fibrations on spheres, extending concepts from holomorphic functions.

Contribution

It introduces a comparison framework for Milnor fibrations of meromorphic functions, extending the classical holomorphic case to a broader class of functions.

Findings

Establishes a relationship between local and global Milnor fibrations for meromorphic functions.

Provides new insights into the topology of meromorphic function singularities.

Extends Milnor fibration theory beyond holomorphic functions.

Abstract

In analogy with the holomorphic case, we compare the topology of Milnor fibrations associated to a meromorphic germ f/g : the local Milnor fibrations given on Milnor tubes over punctured discs around the critical values of f/g, and the Milnor fibration on a sphere.