Louis Kauffman, Classical and virtual knot theory (lecture 10)

This course will begin with combinatorial knot theory via the Reidemeister moves, the Kauffman bracket model for the Jones polynomial, the associated Khovanov homology, quantum invariants of knots and links, skein polynomials and the Alexander polynomial. We will study both classical and virtual knot theory. We will consider surfaces that bound knots and links in three and four dimensional space and properties of cobordisms of knots and knotted surfaces in four space. Time permitting, we will cover relationships of knots with physics and with molecular biology. The prerequisites for this course are basic abstract algebra and point set topology. Some acquaintance with algebraic topology is useful background but not required for the course.