We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
30/2009
On the orders of periodic symplectomorphisms of $4$-manifolds
Weimin Chen
Abstract
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.
