Volume 2 (1999)

Download this article
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
MSP Books and Monographs
Other MSP Publications

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