Duke Mathematical Journal

On the orders of periodic diffeomorphisms of 4-manifolds

Weimin Chen

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This paper initiated an investigation on the following question: Suppose that a smooth 4-manifold does not admit any smooth circle actions. Does there exist a constant C>0 such that the manifold supports no smooth Zp-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.

Article information

Duke Math. J. Volume 156, Number 2 (2011), 273-310.

First available in Project Euclid: 2 February 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57S15: Compact Lie groups of differentiable transformations 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
Secondary: 57R17: Symplectic and contact topology


Chen, Weimin. On the orders of periodic diffeomorphisms of $4$ -manifolds. Duke Math. J. 156 (2011), no. 2, 273--310. doi:10.1215/00127094-2010-212. https://projecteuclid.org/euclid.dmj/1296662021

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