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

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 $n\equiv 5,7\mathrm{m}\mathrm{o}\mathrm{d}8$.