There are many intriguing invariants of knots, some only discovered recently. Some of these come from studying the related braids, which lead to extremely interesting groups, relatively simple to define but with open questions. References:
- Wikipedia Braid group
- Epple, M 1998 Orbits of Asteroids, a Braid, and the First Link Invariant Mathematical Intelligencer, volume 20, number 1, pages 45-52.
- Prasolov, VV and Sossinsky, AB 1997 Knots, Links, Braids, and 3-Manifolds American Mathematical Society.
Supervisor: Professor Stephen Huggett