Date of Graduation
5-2016
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
Jeremy Van Horn-Morris
Committee Member
Allan Cochran
Second Committee Member
Chaim Goodman-Strauss
Third Committee Member
Yo'av Rieck
Keywords
Pure sciences, Arc index, Grid diagrams, Rectangular diagrams, Thurston-bennequin number
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.
Citation
Thomas, E. G. (2016). The Maximal Thurston-Bennequin Number on Grid Number n Diagrams. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/1540