Geometry & Topology Monographs 2 (1999),
Proceedings of the Kirbyfest,
paper no. 25, pages 555-562.
Positive links are strongly quasipositive
Lee Rudolph
Abstract.
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.
Keywords.
Almost positive link, Murasugi sum, positive link, quasipositivity, Seifert's algorithm
AMS subject classification.
Primary: 57M25.
Secondary: 32S55, 14H99.
E-print: arXiv:math.GT/9804003
Submitted: 31 July 1998.
(Revised: 18 March 1999.)
Published: 21 November 1999.
Notes on file formats
Lee Rudolph
Department of Mathematics, Clark University, Worcester MA 01610, USA
Email: lrudolph@black.clarku.edu
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