Knots, Isotopies, and Khovanov Homology Hilary Hunt

Hilary Hunt's 2014 honours thesis in mathematics, on "Knots, isotopies, and Khovanov homology", is available here, along with two auxiliary Mathematica files containing implementations of the Yamada-Vogel algorithm and Khovanov homology.


In this thesis, we aim to investigate the action of the centraliser of a braid on the Khovanov homology of its trace closure. To this end, we explore the theory of knots and braids. We define both objects and clarify the relationship between them. We investigate link invariants including the Jones polynomial and Khovanov homology and look at the uniqueness of isotopies on both braids and links.

last modified: 2014-10-24