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

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
37
Issue
2
Identifiers
DOI: 10.1016/0166-8641(90)90057-9
Disciplines
  • Mathematics

Abstract

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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