Bennequin’s inequality and the positivity of the signature

Stoimenow, A.

doi:10.1090/S0002-9947-08-04410-3

Bennequin’s inequality and the positivity of the signature
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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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