Non-smoothable Four-manifolds with Infinite Cyclic Fundamental Group Academic Article uri icon

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abstract

  • 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.

publication date

  • January 1, 2007