Non-smoothable Four-manifolds with Infinite Cyclic Fundamental Group

In [11], two of us constructed a closed oriented 4-dimensional manifold with fundamental group ℤ that does not split off S1 × S3. In this note we show that this 4-manifold, and various others derived from it, do not admit smooth structures. Moreover, we find an infinite family of 4-manifolds with exactly the same properties. As a corollary, we obtain topologically slice knots that are not smoothly slice in any rational homology ball.