## Rohlin’s theorem and non-simply connected 4-manifolds

Most applications of gauge theory in 4-dimensional topology are concerned with simply-connected manifolds with non-trivial second homology. I will discuss the opposite situation, first describing the classical Rohlin invariant for manifolds with first homology = Z and vanishing second homology. I will give an interpretation in terms of a Seiberg-Witten theory, with an unusual index-theoretic correction term. I will discuss recent work with Jianfeng Lin and Nikolai Saveliev giving a new formula for this invariant in terms of monopole homology.