Free circle actions on $(n-1)$-connected $(2n+1)$-manifolds

TL;DR

This paper classifies certain high-dimensional manifolds with specific connectivity and homology properties that admit free circle actions, focusing on cases where the dimension parameter satisfies particular modular conditions.

Contribution

It provides a classification of $(n-1)$-connected $(2n+1)$-manifolds with torsion-free homology admitting free circle actions for specific values of $n$ modulo 8.

Findings

Identifies manifolds admitting free circle actions for $n ot\equiv 0, 1 mod 8$

Classifies these manifolds up to almost diffeomorphism

Focuses on torsion-free homology cases

Abstract

In this paper, we determine those $(n-1)$-connected $(2n+1)$-manifolds with torsion free homology that admit free circle actions up to almost diffeomorphism, provided that $n\equiv5,7 \mod 8$.