## Cyclic group actions and embedded spheres in 4-manifolds

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**144**(2016), 411-422 Request permission

## Abstract:

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.## References

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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: mark.hamilton@math.lmu.de
- 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: https://doi.org/10.1090/proc/12707
- MathSciNet review: 3415607