Journal of the Mathematical Society of Japan

On the Seifert form at infinity associated with polynomial maps

András NÉMETHI

Full-text: Open access

Abstract

If apolynomial map f : CnC has anice behaviour at infinity (e.g. it is a "good polynomial"), then the Milnor fibration at infinity exists; in particular, one can define the Seifert form at infinity Γ(f) associated with f. In this paper we prove a Sebastiani-Thom type formula. Namely, if f : CnC and g:cmC are "good" polynomials, and we define h=fg : Cn+mC by h(x,y)=f(x)+g(y), then Γ(h)=(-I)mnΓ(f)Γ(g). This is the global analogue of the local result, proved independently by K. Sakamoto and P. Deligne for isolated hypersurface singularities.

Article information

Source
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 63-70.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213108351

Digital Object Identifier
doi:10.2969/jmsj/05110063

Mathematical Reviews number (MathSciNet)
MR1660996

Zentralblatt MATH identifier
0933.32042

Subjects
Primary: 14F45: Topological properties
Secondary: 14D25 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45] 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}

Keywords
Good polynomials Milnor fibrations at infinity Seifert forms variation map spinnable structures open book decomposition

Citation

NÉMETHI, András. On the Seifert form at infinity associated with polynomial maps. J. Math. Soc. Japan 51 (1999), no. 1, 63--70. doi:10.2969/jmsj/05110063. https://projecteuclid.org/euclid.jmsj/1213108351


Export citation