### On the orders of periodic diffeomorphisms of $4$-manifolds

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

#### 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.

First Page:
Primary Subjects: 57S15, 57R57
Secondary Subjects: 57R17
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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

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