On the orders of periodic symplectomorphisms of 4-manifolds
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Submission date: 13. Jul. 2009
MSC-Numbers: 57S15, 57R57, 57R17
Keywords and phrases: Bound of automorphisms, smooth four-manifolds, symplectic
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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 with and , the order of a periodic symplectomorphism of prime order is bounded from above by a constant C, which depends on in a rather unstable way.