Classification of homotopy Wallʹs manifolds

Complete PL and topological classification and partial smooth classification of manifolds homotopy equivalent to a Wallʹs manifold (defined as a mapping torus of a Dold manifold), introduced by Wall in his 1960 Annals paper on cobordism, have been done by determining: (1) the normal invariants of Wallʹs manifolds, (2) the surgery obstruction of a normal invariant and (3) the action of the Wall surgery obstruction groups on the smooth, PL and homeomorphism classes of homotopy Wallʹs manifolds (to be made precise in the body of the paper). Consequently classification results of automorphisms (self homeomorphisms, and self PL-homeomorphisms) of Dold manifolds follow.