The Bennequin number of n-trivial closed n-braids is negative
classification
🧮 math.GT
math.SG
keywords
bennequinclosedn-braidsn-trivialnegativenumberresultbraid
read the original abstract
A famous result of Bennequin states that for any braid representative of the unknot the Bennequin number is negative. We will extend this result to all n-trivial closed n-braids. This is a class of infinitely many knots closed under taking mirror images. Our proof relies on a non-standard parametrization of the Homfly polynomial.
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