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ISSN (electronic): 1464-8997
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Positive links are strongly quasipositive

Lee Rudolph

Geometry & Topology Monographs 2 (1999) 555–562

DOI: 10.2140/gtm.1999.2.555

arXiv: math.GT/9804003


Let S(D) be the surface produced by applying Seifert's algorithm to the oriented link diagram D. I prove that if D has no negative crossings then S(D) is a quasipositive Seifert surface, that is, S(D) embeds incompressibly on a fiber surface plumbed from positive Hopf annuli. This result, combined with the truth of the ``local Thom Conjecture'', has various interesting consequences; for instance, it yields an easily-computed estimate for the slice euler characteristic of the link L(D) (where D is arbitrary) that extends and often improves the ``slice–Bennequin inequality'' for closed-braid diagrams; and it leads to yet another proof of the chirality of positive and almost positive knots.

For Rob Kirby


almost positive link, Murasugi sum, positive link, quasipositivity, Seifert's algorithm

Mathematical Subject Classification

Primary: 57M25

Secondary: 14H99, 32S55


Received: 31 July 1998
Revised: 18 March 1999
Published: 21 November 1999

Lee Rudolph
Department of Mathematics
Clark University
Worcester MA 01610