On the orders of periodic diffeomorphisms of 4-manifolds

Weimin Chen

doi:10.1215/00127094-2010-212

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arXiv · 0907.5343

On the orders of periodic diffeomorphisms of 4-manifolds

Weimin Chen

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Abstract

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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Weimin Chen. 2009-07-30. On the orders of periodic diffeomorphisms of 4-manifolds. https://doi.org/10.1215/00127094-2010-212

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