English

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.

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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