Math 661 — Fall 2001 Geometric Topology: Knot Theory

Text:On Knots, by Louis Kauffman (Princeton University Press).

Knot theory is the study of embedded loops in three dimensional space up to certain deformations. We will survey a variety of topics in this area, including: Reidemeister moves, seifert surfaces, the braid group, concordance, ribbon versus slice, 2-knots, knot polynomials (Conway, Jones...), n-colorings, arf invariant, seifert form and S-equivalence, Milnor's link homotopy, elementary Vassiliev theory, virtual knots, knot groups, quandles, wild knots.