Document Type
Article
Publication Date
1-1-2001
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 parameterization of the HOMFLY polynomial. Another interesting corollary of this parameterization is that if all Vassiliev invariants up to degree c vanish on a knot of crossing number c, then this knot has trivial HOMFLY polynomial.
Publication Source (Journal or Book title)
Mathematical Research Letters
First Page
629
Last Page
635
Recommended Citation
Dasbach, O., & Xiao-Song, L. (2001). The Bennequin number of n-trivial closed n-braids is negative. Mathematical Research Letters, 8 (5-6), 629-635. https://doi.org/10.4310/MRL.2001.v8.n5.a4
