Cyclic group actions and embedded spheres in 4-manifolds
Geometric Topology
2019-03-05 v3 Algebraic Topology
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.
Cite
@article{arxiv.1406.2986,
title = {Cyclic group actions and embedded spheres in 4-manifolds},
author = {M. J. D. Hamilton},
journal= {arXiv preprint arXiv:1406.2986},
year = {2019}
}
Comments
13 pages; to appear in Proc. Amer. Math. Soc