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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Bennequin’s inequality and the positivity of the signature
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by A. Stoimenow PDF
Trans. Amer. Math. Soc. 360 (2008), 5173-5199 Request permission

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
  • Received by editor(s): June 28, 2006
  • Published electronically: May 27, 2008
  • Additional Notes: The author was supported by the 21st Century COE Program
  • © Copyright 2008 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5173-5199
  • MSC (2000): Primary 57M25; Secondary 57N70
  • DOI: https://doi.org/10.1090/S0002-9947-08-04410-3
  • MathSciNet review: 2415070