Homology manifolds and euclidean bundles

We construct a Poincaré complex whose periodic total surgery obstruction vanishes but whose Spivak normal fibration does not admit a reduction to a stable euclidean bundle.

This contradicts the conjunction of two claims in the literature: Namely, on the one hand that a Poincaré complex with vanishing periodic total surgery obstruction is homotopy equivalent to a homology manifold, which appears in work of Bryant, Ferry, Mio and Weinberger, and on the other that the Spivak normal fibration of a homology manifold always admits a reduction to a stable euclidean bundle, which appears in work of Ferry and Pedersen.