(Department of Mathematics, University of Manitoba)
Knot Groups and Orderability
|Date||Friday, March 7, 2014|
I'll give a quick introduction to knots and knot groups, and briefly give an algorithm for calculating the group of a knot. By associating a group to every knot in the prescribed way, knot theoretic questions of a topological nature are translated into algebraic questions (and vice versa).
This bijection between knots and groups makes certain natural algebraic questions interesting to knot theorists, and recently questions of knot group orderability have become more prominent in the field. I'll give a summary of what is known, and outline the direction of current research.