The singularities of the maps associated with Milnor fibrations

TL;DR

This paper investigates the singularities of Milnor fibration product maps, providing a characterization of singular points and criteria for fold points in the context of weighted homogeneous polynomials.

Contribution

It introduces a new analysis of singular points in Milnor fibration product maps and offers criteria for fold points with their indices for specific polynomial classes.

Findings

Characterization of singular points of Milnor fibration product maps

Criterion for fold points in weighted homogeneous polynomials

Identification of indices for fold points

Abstract

Milnor fibrations have been studied since 1960's. In this paper, we study singular points of differentiable maps, called Milnor fibration product maps, obtained by several Milnor fibrations. We give a characterization of singular points of such product maps, and for the case of certain weighted homogeneous polynomials, a criterion for a fold point together with its index.