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Cyclic group actions and embedded spheres in 4-manifolds


Author: M. J. D. Hamilton
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
Published electronically: July 24, 2015
MathSciNet review: 3415607
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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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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

DOI: https://doi.org/10.1090/proc/12707
Keywords: 4-manifold, group action, fixed point set, $G$-signature theorem
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
Article copyright: © Copyright 2015 American Mathematical Society