The Maximal Thurston-Bennequin Number on Grid Number n Diagrams

<p>We will prove an upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.</p> <p>TB(n)=CR(n)-[n/2]</p> <p>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.</p>

Name thesis:degree_name

Doctor of Philosophy in Mathematics (PhD)

Level thesis:degree_level

Dissertation

Year dc:date.available

2016

Author dc:creator

• Thomas, Emily Goins

Advisor dc:contributor.advisor

• Van Horn-Morris, Jeremy

Contributors dc:contributor

• Cochran, Allan
• Goodman-Strauss, Chaim

• Pure sciences
• Arc index
• Grid diagrams
• Rectangular diagrams
• Thurston-bennequin number
• Other Applied Mathematics

Repository record dc:identifier

https://scholarworks.uark.edu/etd/1540

OAI identifier oai:identifier

oai:scholarworks.uark.edu:etd-3079