The Bennequin number of n-trivial closed n-braids is negative

Details The Bennequin number of n-trivial closed n-braids is negative The Bennequin number of n-trivial closed n-braids is negative

2000-10-27

arxiv.org/abs/math/0010278v1

Math. Res. Lett. 8 (2001), no. 5-6, 629--635

Mathematics

Geometric Topology

7 pages

Scientific paper

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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