Knots, Braids, and Knot Invariants
Geometric Topology
2022-02-15 v1 Rings and Algebras
Abstract
In this report, I will start by first giving a brief introduction on knots to build some intuition before beginning the more rigorous review in the Literature Review section. There, I will define knot equivalence, the Jones polynomial invariant, braid groups, Hecke algebras, and the HOMFLY polynomial invariant. Next, I will cover some of my independent research regarding the computation of a general formula for the HOMFLY polynomial of the closure of looped coxeter braids. Lastly, I will loosely discuss how this research connects to future research regarding the universal trace in the Plan for Future Work section.
Keywords
Cite
@article{arxiv.2202.06118,
title = {Knots, Braids, and Knot Invariants},
author = {Matthew Stevens},
journal= {arXiv preprint arXiv:2202.06118},
year = {2022}
}