Detecting codimension one manifold factors with the disjoint homotopies property

Codimension one manifold factors are spaces which have the property that their product with R is a manifold. In this paper, the disjoint homotopies property (DHP) is introduced and it is shown that resolvable generalized manifolds with DHP are codimension one manifold factors. For generalized manifolds of dimensions n⩾4 it is shown that DHP is implied by the plentiful 2-manifolds property, a property satisfied by many examples. Furthermore, a new class of codimension one manifold factors, the k-ghastly spaces for k>2, is constructed.