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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bennequin's inequality and the positivity of the signature


Author: A. Stoimenow
Journal: Trans. Amer. Math. Soc. 360 (2008), 5173-5199
MSC (2000): Primary 57M25; Secondary 57N70
Published electronically: May 27, 2008
MathSciNet review: 2415070
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Abstract: We use an algorithm for special diagrams to prove a Bennequin type inequality for the signature of an arbitrary link diagram, related to its Murasugi sum decomposition. We apply this inequality to show that the signature of a non-trivial positive 3-braid knot is greater than its genus, and that the signature of a positive braid link is minorated by an increasing function of its negated Euler characteristic. The latter property is conjectured to extend to positive links.


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Additional Information

A. Stoimenow
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Address at time of publication: Department of Mathematical Sciences, BK21 Project, KAIST, Daejeon, 307-701 Korea
Email: stoimeno@kurims.kyoto-u.ac.jp, alexander@stoimenov.net

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04410-3
PII: S 0002-9947(08)04410-3
Keywords: Signature, genus, positive braid, positive link, special diagram, topological concordance, Bennequin inequality
Received by editor(s): June 28, 2006
Published electronically: May 27, 2008
Additional Notes: The author was supported by the 21st Century COE Program
Article copyright: © Copyright 2008 American Mathematical Society