Abstract
We give several criteria on a closed, oriented 3 3 -manifold that will imply that it is the boundary of a (simply connected) 4 4 -manifold that admits infinitely many distinct smooth structures. We also show that any weakly fillable contact 3 3 -manifold, or contact 3 3 -manifold with non-vanishing Heegaard Floer invariant, is the boundary of a simply connected 4 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.
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