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

Abstract

Abstract In this paper we study smooth orientation-preserving free actions of the cyclic group ℤ / m {\mathbb{Z}/m} on a class of ( n - 1 ) {(n-1)} -connected 2 ⁢ n {2n} -manifolds, ♯ ⁡ ♯ ⁡ g ⁢ ( S n × S n ) Σ {\mathbin{\sharp}g(S^{n}\times S^{n})\mathbin{\sharp}\Sigma} , where Σ is a homotopy 2 ⁢ n {2n} -sphere. When n = 2 {n=2} , we obtain a classification up to topological conjugation. When n = 3 {n=3} , we obtain a classification up to smooth conjugation. When n ≥ 4 {n\geq 4} , we obtain a classification up to smooth conjugation when the prime factors of m are larger than a constant C ⁢ ( n ) {C(n)} .