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MiS Preprint

On the orders of periodic symplectomorphisms of $4$-manifolds

Weimin Chen


In this paper we investigate generalizations of the classical Hurwitz theorem concerning bound of the order of automorphism group of a Riemann surface of genus at least two to smooth $4$-manifolds. In particular, it is shown that for a simply connected symplectic $4$-manifold $(X,\omega)$ with $b_2^{+}>1$ and $[\omega]\in H^2(X;Q)$, the order of a periodic symplectomorphism of prime order is bounded from above by a constant $C$, which depends on $\omega$ in a rather unstable way.

MSC Codes:
57S15, 57R57, 57R17
Bound of automorphisms, smooth four-manifolds, symplectic

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2009 Repository Open Access
Weimin Chen

On the orders of periodic symplectomorphisms of 4-manifolds