Results on Milnor Fibrations for mixed polynomials with non-isolated singularities

TL;DR

This paper investigates conditions under which mixed polynomials with non-isolated singularities admit Milnor fibrations, establishing fiber homeomorphisms and criteria for transversality in specific polynomial classes.

Contribution

It provides new criteria for the existence of Milnor and Milnor-L extsuperscript{e} fibrations in mixed polynomials with non-isolated singularities, and proves fiber homeomorphism results.

Findings

Milnor-L extsuperscript{e} fiber homeomorphism between regular and critical values

A transversality criterion for mixed polynomials

Application of criteria to a specific class of mixed polynomials

Abstract

In this article we investigate mixed polynomials and present conditions that can be applied on a specific class of polynomials in order to prove the existence of the Milnor Fibration, Milnor-L\^e Fibration and the equivalence between them. We prove for this class the of functions that the Milnor-L\^e fiber on a regular value is homeomorphic to the Milnor-L\^e fiber on a critical value. We develop a criterion to verify the transversality property and apply it to a special case of the class of mixed polynomial.