Knots and their Invariants
Abstract: This short course of 5 lectures will be a basic introduction to the study
of knots and their invariants. After discussing the necessary knot theory basics,
topics will be chosen from
1) Torus and satellite knots; braids and their connection to knots
2) Quantum mechanics, the Kauffman bracket, and polynomial invariants; Vassiliev invariants
3) Knot complements and three manifolds; Seifert surfaces and the genus of a knot;
hyperbolic geometry, Mostow-Prasad rigidity, and applications to knot complements;
software designed to compute hyperbolic invariants of knots.