We obtain a classification of tame manifold neighborhoods of compact ENR
homology manifolds in codimension greater than 2 (or equivalently,
manifold approximate fibrations with spherical fibers), extending the results
of Rourke and Sanderson for topological manifolds. As applications, we
obtain analogues of Browder's theorem on smoothings and triangulations of
Poincaré embeddings, and of the Casson-Haefliger-Sullivan-Wall embedding
theorem for homology manifolds.