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The Maximal Thurston-Bennequin Number On Grid Number N Diagrams, Emily Goins Thomas
The Maximal Thurston-Bennequin Number On Grid Number N Diagrams, Emily Goins Thomas
Graduate Theses and Dissertations
We will prove an upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.
TB(n)=CR(n)-[n/2]
In order to prove the bound, we will separate our work for when n is even and when n is odd. After we prove the upper bound, we will show that there are unique knots and links on each grid which achieve the upper bound. When n is even, torus links achieve the maximum, and when n is odd, torus knots achieve the maximum.