ON 3-MANIFOLDS THAT ARE BOUNDARIES OF EXOTIC 4-MANIFOLDS

We give several criteria on a closed, oriented 3-manifold that will imply that it is the boundary of a (simply connected) 4-manifold that admits infinitely many distinct smooth structures. We also show that any weakly fillable contact 3-manifold, or contact 3-manifold with non-vanishing Heegaard Floer invariant, is the boundary of a simply connected 4-manifold that admits infinitely many distinct smooth structures each of which supports a symplectic structure with concave boundary, that is there are infinitely many exotic caps for any such contact manifold.