The main concern of this project is to study smooth simply connected 4-manifolds by using invariants obtained from gauge theory. In particular, the investigator wishes to use 2-torsion instanton invariants to study the result of taking connected sums with S2 x S2. Using the relation of these torsion invariants with the usual Donaldson invariants and using Z2-invariant theory, the investigator hopes to deduce universal relations for certain Donaldson invariants. He also plans to search for the proper setting for relative torsion invariants. The interactions of this project with mathematical physics go both ways. On the one hand, four-dimensional manifolds are cosmologically important, since we live in a manifold of three space dimensions and one time dimension. On the other hand, and more surprisingly, notions from quantum mechanics have led to new topological invariants of manifolds.
