Duke Mathematical Journal

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 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 ${\mathbb Z}_p$-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.

Article information

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

Dates
First available in Project Euclid: 2 February 2011

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1296662021

Digital Object Identifier
doi:10.1215/00127094-2010-212

Zentralblatt MATH identifier
05858725

Mathematical Reviews number (MathSciNet)
MR2769218

Subjects
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

Citation

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


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