Open Access
January, 2014 On the enhancement to the Milnor number of a class of mixed polynomials
Kazumasa INABA
J. Math. Soc. Japan 66(1): 25-36 (January, 2014). DOI: 10.2969/jmsj/06610025


The enhancement to the Milnor number is an invariant of the homotopy classes of fibered links in the sphere $S^{2n-1}$ and belongs to $\mathbb{Z}/r\mathbb{Z}$, where $r=0$ if $n=2$ and $r=2$ if $n=2$. Mixed polynomials are polynomials in complex variables $z_1,\dots,z_n$ and their conjugates $\bar{z}_1,\dots,\bar{z}_n$. 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 $\mathbb{Z}/r\mathbb{Z}$ is realized by the enhancement to the Milnor number of such a fibered link.


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Kazumasa INABA. "On the enhancement to the Milnor number of a class of mixed polynomials." J. Math. Soc. Japan 66 (1) 25 - 36, January, 2014.


Published: January, 2014
First available in Project Euclid: 24 January 2014

zbMATH: 1296.14028
MathSciNet: MR3161391
Digital Object Identifier: 10.2969/jmsj/06610025

Primary: 14J17
Secondary: 37C27 , 58K45

Keywords: enhanced Milnor number , fibered link , mixed polynomial

Rights: Copyright © 2014 Mathematical Society of Japan

Vol.66 • No. 1 • January, 2014
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