Date of Graduation
Doctor of Philosophy in Mathematics (PhD)
Jeremy Van Horn-Morris
Second Committee Member
Third Committee Member
Pure sciences; Arc index; Grid diagrams; Rectangular diagrams; Thurston-bennequin number
We will prove an upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.
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.
Thomas, Emily Goins, "The Maximal Thurston-Bennequin Number on Grid Number n Diagrams" (2016). Theses and Dissertations. 1540.