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Bulletin of the London Mathematical Society 1995 27(4):387-391; doi:10.1112/blms/27.4.387
© 1995 by London Mathematical Society
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© London Mathematical Society

Free Products and 4-Dimensional Connected Sums

Jonathan A. Hillman

School of Mathematics and Statistics, University of Sydney Sydney, NSW 2006, Australia

Received 12 July 1993.

We show that a closed 4-manifold whose fundamental group is a nontrivial free product is stably homeomorphic to one which admits a corresponding decomposition into a connected sum, and that connected sums of copies of S1 x S3 and S1 x S3 may be characterized up to s-cobordism by their fundamental group, Euler characteristic and orientability. These results are applied to obtain weak splitting and triviality theorems for links in S4.


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