Abstract
How many ways can you embed a circle in 3-space? This question is what motivates most of knot theory, and the first part of this presentation. Following a primer on the basics of knots, I will introduce some widely used knot invariants, from the Alexander and the Kauffman, to the Vasilievs and the Khovanov. Of the stronger ones, Vasiliev's invariants have a very combinatorial flavor, through the use of chord diagrams, while Khovanov's has a distinctly homological structure. Finally, if time permits, I will describe braid groups and the power that comes with this formalized approach.
Resources
- Slides of the talk
- Course notes from a knot theory course I took
- The Knot Atlas, an online knot encyclopedia
- KnotPlot, a program for drawing, viewing and playing with knots
This page was last updated on 22.05.2014 at 23:02 EDT