Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
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.
