Plumbing constructions of connected divides and the Milnor fibers of plane curve singularities

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A divide is the image of a generic, relative immersion of a finite number of copies of the unit interval or the unit circle into the unit disk. N. A'Campo defined for each connected divide a link in S3 and proved that the link is fibered. In the present paper we show that the fiber surface of the fibration of a connected divide can be obtained from a disk by a successive plumbing of a finite number of positive Hopf bands. In particular, this gives us a geometric understanding of plumbing constructions of the Milnor fibers of isolated, complex plane curve singularities in terms of certain replacements of the curves of their real modifications.

Original languageEnglish
Pages (from-to)499-514
Number of pages16
JournalIndagationes Mathematicae
Volume13
Issue number4
DOIs
Publication statusPublished - 2002 Jan 1
Externally publishedYes

Fingerprint

Milnor Fiber
Plane Curve
Divides
Singularity
Fibration
Unit circle
Immersion
Argand diagram
Unit Disk
Replacement
Fiber
Curve
Interval
Unit

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Plumbing constructions of connected divides and the Milnor fibers of plane curve singularities. / Ishikawa, Masaharu.

In: Indagationes Mathematicae, Vol. 13, No. 4, 01.01.2002, p. 499-514.

Research output: Contribution to journalArticle

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