Title

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

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

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