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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Cyclic group actions and embedded spheres in 4-manifolds
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by M. J. D. Hamilton PDF
Proc. Amer. Math. Soc. 144 (2016), 411-422 Request permission


In this note we derive an upper bound on the number of 2-spheres in the fixed point set of a smooth and homologically trivial cyclic group action of prime order on a simply-connected 4-manifold. This improves the a priori bound which is given by one half of the Euler characteristic of the 4-manifold. The result also shows that in some cases the 4-manifold does not admit such actions of a certain order at all or that any such action has to be pseudofree.
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Additional Information
  • M. J. D. Hamilton
  • Affiliation: Institute for Geometry and Topology, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
  • Email:
  • Received by editor(s): July 29, 2014
  • Received by editor(s) in revised form: December 4, 2014
  • Published electronically: July 24, 2015
  • Communicated by: Martin Scharlemann
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 411-422
  • MSC (2010): Primary 57M60, 57S17, 57N13; Secondary 57R57
  • DOI:
  • MathSciNet review: 3415607