On the enhancement to the Milnor number of a class of mixed polynomials

Abstract

The enhancement to the Milnor number is an invariant of the homotopy classes of fibered links in the sphere S²ⁿ⁻¹ and belongs to ℤ⁄rℤ, where r = 0 if n = 2 and r = 2 if n = 2. Mixed polynomials are polynomials in complex variables z₁,…,z_n and their conjugates $¥bar{z}$₁,…,$¥bar{z}$_n. M. Oka showed that mixed polynomials have Milnor fibrations under the strongly non-degeneracy condition. In this present paper, we study fibered links which are defined by a certain class of mixed polynomials which admit Milnor fibrations and show that any element of ℤ⁄rℤ is realized by the enhancement to the Milnor number of such a fibered link.