Geometric Topology and Field Theory

The interaction between the geometric topology of low dimensional manifolds and classical and quantum field theories began with a few special results in the early 1980s. It has since developed into a very active area of research in both mathematics and physics. In Lecture I, we will review the early and by now well established results for dimensions 3 and 4. In the second lecture we will discuss the various homology theories associated to knots and links in 3-manifolds. If time permits, we will also consider the relation between WRT invariants and topological string amplitudes.

For some background, see my MPI webprints 45/2004, 53/2000, and references there.