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 ${\displaystyle M^3}$ may be obtained by an (n/1)-Dehn surgery on a homology 3-sphere if and only if the linking form of ${\displaystyle M^3}$ 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.