HOMOLOGY LENS SPACES AND DEHN SURGERY ON HOMOLOGY SPHERES

A homology lens space is a closed 3-manifold with Z-homology groups isomorphic to those of a lens space. A useful theorem found in [Fu] states that a homology lens space M3 may be obtained by an (n/1)-Dehn surgery on a homology 3-sphere if and only if the linking form of M3 is equivalent to (1/n). In this note we generalize this result to cover all homology lens spaces, and in the process offer an alternative proof based on classical 3-manifold techniques.