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Bulletin of the London Mathematical Society Advance Access originally published online on March 21, 2007
Bulletin of the London Mathematical Society 2007 39(2):327-328; doi:10.1112/blms/bdl042
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© 2007 London Mathematical Society

On 4-manifolds with zero-entropy metrics

J. A. Hillman

School of Mathematics and Statistics
University of Sydney
NSW 2006
Australia
jonh{at}maths.usyd.edu.au

Received 23 November 2005. Revision received 24 May 2006.

We sharpen a recent result of Paternain and Petean by showing that a closed 4-manifold which admits a Riemannian metric with zero topological entropy and infinite fundamental group either is aspherical or has a finite covering space homeomorphic to S3 x S1 or S2 x S1 x S1.


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