Geometry & Topology Monographs 2 (1999),
Proceedings of the Kirbyfest,
paper no. 25, pages 555-562.
Positive links are strongly quasipositive
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.
Almost positive link, Murasugi sum, positive link, quasipositivity, Seifert's algorithm
AMS subject classification.
Secondary: 32S55, 14H99.
Submitted: 31 July 1998.
(Revised: 18 March 1999.)
Published: 21 November 1999.
Notes on file formats
Department of Mathematics, Clark University, Worcester MA 01610, USA
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