Non-smoothable four-manifolds with cyclic fundamental group

Stefan Friedl, Ian Hambleton, Paul Melvin, Peter Teichner

Published 2006-11-03, updated 2007-03-10Version 2

In [HT], two of us constructed a closed oriented 4-dimensional manifold with fundamental group $\Z$ that does not split off $S^1\times S^3$. 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 (and same intersection form on $H_2$). As a corollary, we obtain topologically slice knots that are not smoothly slice in any rational homology ball.