The Bennequin number of n-trivial closed n-braids is negative
Geometric Topology
2007-06-13 v1 Symplectic Geometry
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.
Cite
@article{arxiv.math/0010278,
title = {The Bennequin number of n-trivial closed n-braids is negative},
author = {Oliver T. Dasbach and Xiao-Song Lin},
journal= {arXiv preprint arXiv:math/0010278},
year = {2007}
}
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7 pages