Embeddings of Homology Manifolds in Codimension > = 3   (J. Bryant and W. Mio)

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.

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