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

TL;DR

This paper classifies free cyclic group actions on highly-connected 2n-manifolds, providing topological and smooth classifications depending on dimension and prime factors of the group order.

Contribution

It offers new classifications of free cyclic group actions on certain high-dimensional manifolds, extending understanding in both topological and smooth categories.

Findings

Classification up to topological conjugation for n=2

Classification up to smooth conjugation for n=3

Smooth classification for n≥4 when prime factors of m are large

Abstract

In this paper we study smooth orientation-preserving free actions of the cyclic 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 topological conjugation. When $n=3$ we obtain a classification up to smooth conjugation. When $n \ge 4$ we obtain a classification up to smooth conjugation when the prime factors of $m$ are larger than a constant $C(n)$.