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ALMOST ALTERNATING DIAGRAMS AND FIBERED LINKS IN S3

Published online by Cambridge University Press:  23 August 2001

HIROSHI GODA ,
MIKAMI HIRASAWA  and
RYOSUKE YAMAMOTO
HIROSHI GODA
Affiliation:
Kobe University, Current address:, Department of Mathematics, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho Koganei-city, Tokyo 184-8588, Japan, goda@cc.tuat.ac.jp
MIKAMI HIRASAWA
Affiliation:
Osaka University, Current address:, Department of Mathematics, Faculty of Science, Gakushuin University, 1-5-1, Mejiro Toshima, Tokyo 171-8588, Japan, hirasawa@math.gakushuin.ac.jp
RYOSUKE YAMAMOTO
Affiliation:
Kobe University, Current address:, Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka 560-0043, Japan, ryosuke@math.kobe-u.ac.jp
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Abstract

Let R be a Seifert surface obtained by applying Seifert's algorithm to a connected diagram D for a link L. In this paper, letting D be almost alternating, we give a practical algorithm to determine whether L is a fibered link and R is a fiber surface. We further show that L is a fibered link and R is a fiber surface for L if and only if R is a Hopf plumbing, that is, a successive plumbing of a finite number of Hopf bands. It has been known for some time that this is true if D is alternating, and we show that it is not always true if D is 2-almost alternating. In the appendix, we partially answer C. Adams's open question concerning almost alternating diagrams.

2000 Mathematical Subject Classification: 57M25.

Keywords

fibered linksalmost alternating diagramsMurasugi sumHopf plumbing
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 83 , Issue 2 , September 2001 , pp. 472 - 492
Copyright
2001 London Mathematical Society

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