This paper initiated an investigation on the following question: Suppose that a smooth -manifold does not admit any smooth circle actions. Does there exist a constant such that the manifold supports no smooth -actions of prime order for ? We gave affirmative results to this question for the case of holomorphic and symplectic actions, with an interesting finding that the constant in the holomorphic case is topological in nature, while in the symplectic case it involves also the smooth structure of the manifold.
"On the orders of periodic diffeomorphisms of -manifolds." Duke Math. J. 156 (2) 273 - 310, 1 February 2011. https://doi.org/10.1215/00127094-2010-212