  This paper initiated an investigation on the following question: Suppose a
smooth 4-manifold does not admit any smooth circle actions. Does there exist a
constant $C>0$ such that the manifold support no smooth $\Z_p$-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.

Geometric Topology;Symplectic Geometry