Cyclic group actions and embedded spheres in 4-manifolds

Hamilton, M.

doi:10.1090/proc/12707

Cyclic group actions and embedded spheres in 4-manifolds
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by M. J. D. Hamilton

Proc. Amer. Math. Soc. 144 (2016), 411-422

DOI: https://doi.org/10.1090/proc/12707

Published electronically: July 24, 2015

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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.

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