Invariants of Smooth Four-Manifolds: Topology, Geometry, Physics

Abstract

The profound and beautiful interaction between smooth four-manifold topology and the quantum theory of fields often seems as impenetrable as it is impressive. The objective of this series of lectures is to provide a very modest introduction to this interaction by describing, in terms as elementary as possible, how Atiyah and Jeffrey [1] came to view the partition function of Witten’s first topological quantum field theory [21], which coincides with the zero-dimensional Donaldson invariant, as an “Euler characteristic” for an infinite-dimensional vector bundle.