On the orders of periodic diffeomorphisms of 4-manifolds

Details On the orders of periodic diffeomorphisms of 4-manifolds On the orders of periodic diffeomorphisms of 4-manifolds

2009-07-30

arxiv.org/abs/0907.5343v2

Mathematics

Geometric Topology

30 pages, no figures, final version, with a slightly changed title, to appear in Duke Math. J

Scientific paper

This paper initiated an investigation on the following question: Suppose a smooth 4-manifold does not admit any smooth circle actions. Does there exist a constant $C>0$ such that the manifold support no smooth $\Z_p$-actions of prime order for $p>C$? We gave affirmative results to this question for the case of holomorphic and symplectic actions, with an interesting finding that the constant $C$ in the holomorphic case is topological in nature while in the symplectic case it involves also the smooth structure of the manifold.

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