Date of Graduation

5-2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor

Jeremy Van Horn-Morris

Committee Member

Allan Cochran

Second Committee Member

Chaim Goodman-Strauss

Third Committee Member

Yo'av Rieck

Abstract

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.

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