Codimension One or Two Immersions and Submersions of Low Dimensional Manifolds

Let A be a manifold satisfying certain conditions which are weaker than those of E. Thomas, and f: M . N be a map with codimension one or two. We give necessary and suffi cient conditions for f to be homotopic to a map with maximal rank. As an application. we com pletely determine the codimension one or two immersions of Dold manifolds in real projective spaces.