The Witten Conjecture

Abstract

Low-dimensional topology has experienced a number of revolutionary upheavals in the past twenty years. For many of these the seeds of the revolution were sown in theoretical physics and, more particularly, in the work of Edward Witten. The most recent such event occurred in 1994 when Witten suggested that the topological information about smooth 4-manifolds contained in the Donaldson invariants should also be contained in the much simpler and now famous Seiberg–Witten invariants. This lecture will provide an informal survey of some of the background behind the conjecture and how it came to be made.