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