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In this paper we study smooth orientation-preserving free actions of thecyclic group $\mathbb Z/m$ on a class of $(n-1)$-connected $2n$-manifolds,$\sharp g (S^n \times S^n)\sharp \Sigma$, where $\Sigma$ is a homotopy$2n$-sphere. When $n=2$ we obtain a classification up to topologicalconjugation. When $n=3$ we obtain a classification up to smooth conjugation.When $n \ge 4$ we obtain a classification up to smooth conjugation when theprime factors of $m$ are larger than a constant $C(n)$.

Free cyclic group actions on highly-connected $2n$-manifolds