Author ORCID Identifier
0009-0008-5111-7870
Date of Award
Spring 6-9-2024
Document Type
Thesis (Ph.D.)
Department or Program
Mathematics
First Advisor
Vladimir Chernov
Second Advisor
Peter Doyle
Abstract
The Jones polynomial and Khovanov homology are powerful invariants in knot theory. Their computations are known to be NP-Hard and it can be quite a challenge to directly compute either of them for a general knot. We develop explicit algorithms for the Jones polynomial and discuss the implementation of an algorithm for Khovanov homology. Using this we tabulate the invariants for millions of knots, generate statistics on them, and formulate conjectures for Legendrian and transversely simple knots.
Recommended Citation
Maguire, Ryan J., "Khovanov Homology and Legendrian Simple Knots" (2024). Dartmouth College Ph.D Dissertations. 270.
https://digitalcommons.dartmouth.edu/dissertations/270