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

Yang Su 1  and Jianqiang Yang 2
  • 1 School of Mathematics and Systems Science, Chinese Academy of Sciences, 100190; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, P. R. China
  • 2 Department of Mathematics, Honghe University, 661199, Yunnan, P. R. China
Yang Su
  • Corresponding author
  • School of Mathematics and Systems Science, Chinese Academy of Sciences, 100190; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
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and Jianqiang Yang

Abstract

In this paper we study smooth orientation-preserving free actions of the cyclic group /m on a class of (n-1)-connected 2n-manifolds, g(Sn×Sn)Σ, where Σ is a homotopy 2n-sphere. When n=2, we obtain a classification up to topological conjugation. When n=3, we obtain a classification up to smooth conjugation. When n4, we obtain a classification up to smooth conjugation when the prime factors of m are larger than a constant C(n).

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