Classification of homotopy Dold manifolds

摘要

In his Math. Zeitschr. paper of 1956 A. Dold defined manifolds forthe purpose of generating unoriented cobordism groups. In the present paper acomplete piecewise linear and topological classification and partialsmooth classification of manifolds homotopy equivalent to a Doldmanifold have been done by determining: (1) the normal invariants ofthe Dold manifolds, (2) the surgery obstruction of a normal invariantand (3) the action of the Wall surgery obstruction groups on thediffeomorphism, piecewise linear and topological homeomorphism classesof homotopy Dold manifolds (to be made precise in the body of thepaper).