Degree-1 maps into lens spaces and free cyclic actions on homology 3-spheres

AbstractIf M is a closed orientable 3-manifold with H1(M)=Zn, then there is a lens space Ln,m unique up to homotopy, and a degree-1 map ⨍:M→Ln,m. As a corollary we prove that if M̃ is a homology 3-sphere admitting a fixed point free action by Zn, then the regular covering M̃→M̃/Zn is induced from the universal covering S3→Ln,m by a degree-1 map ⨍:M̃/Zn→Ln,m