TY - JOUR

T1 - Plumbing constructions of connected divides and the Milnor fibers of plane curve singularities

AU - Ishikawa, Masaharu

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038307325&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038307325&partnerID=8YFLogxK

U2 - 10.1016/S0019-3577(02)80029-5

DO - 10.1016/S0019-3577(02)80029-5

M3 - Article

AN - SCOPUS:0038307325

VL - 13

SP - 499

EP - 514

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

SN - 0019-3577

IS - 4

ER -