The Bennequin number of n-trivial closed n-braids is negative
Oliver T. Dasbach, Xiao-Song Lin
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.
Create a lesson
Related papers
Linearity of Graph Manifold Groups
Daniel T. Wise
Finding the Birman-Series set
Peter Buser, Hugo Parlier
Thurston's Legacy at the Interface of Surface Dynamics, Train Tracks, and Arithmetic
Ahmad Rafiqi, Ayberk Zeytin
Recognizing oriented knots from finite quotients with one marked element
Indranil Biswas, Shrinit Singh
Symmetries of colored Khovanov-Rozansky homology
Alexis Guérin, Felix Roz
The Colored Jones Function does not determine any colored Links--Gould polynomial
Matthew Harper, Ben-Michael Kohli