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

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.