Journal of the Mathematical Society of Japan

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

Kazumasa INABA

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 1 (2014), 25-36.

Dates
First available in Project Euclid: 24 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1390600835

Digital Object Identifier
doi:10.2969/jmsj/06610025

Mathematical Reviews number (MathSciNet)
MR3161391

Zentralblatt MATH identifier
1296.14028

Subjects
Primary: 14J17: Singularities [See also 14B05, 14E15]
Secondary: 37C27: Periodic orbits of vector fields and flows 58K45: Singularities of vector fields, topological aspects

Keywords
mixed polynomial enhanced Milnor number fibered link

Citation

INABA, Kazumasa. On the enhancement to the Milnor number of a class of mixed polynomials. J. Math. Soc. Japan 66 (2014), no. 1, 25--36. doi:10.2969/jmsj/06610025. https://projecteuclid.org/euclid.jmsj/1390600835


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