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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm031, 20 pages, doi:10.1093/imrn/rnm031 published on Jun 17, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

Non-smoothable Four-manifolds with Infinite Cyclic Fundamental Group

Stefan Friedl1, Ian Hambleton2, Paul Melvin3 and Peter Teichner4,

1 Université du Québec à Montréal, Montréal, Québec
2 McMaster University, Hamilton, Ontario
3 Bryn Mawr College, Bryn Mawr, Pennsylvania
4 University of California, Berkeley, California

Correspondence: Correspondence to be sent to: University of California, Berkeley, California. e-mail: teichner{at}math.berkeley.edu

In [11], two of us constructed a closed oriented 4-dimensional manifold with fundamental group Z that does not split off S1 x 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.

Communicated by Simon K. Donaldson


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