Knot theory, the Jones polynomial and Khovanov homology
Summary
We introduce knot theory in a way suitable for third year Bachelor students. We then introduce the Jones polynomial, an invariant of knots. We `categorize' this Jones polynomial into a chain complex of cobordisms, and then by applying a functor into a chain complex of abelian groups. We can take the homology of this chain complex of groups to get the Khovanov homology.