Real projective spaces are nonfibrators

Fibrators are manifolds which, in context, automatically induce approximate fibrations. This paper sets forth a new method for constructing nonfibrators, by establishing that a closed connected manifold N fails to be a codimension k+1 fibrator provided there exists a homeomorphism h of N×Sk onto itself such that proj·h:N×{point}→N is not a homotopy equivalence. Consequently, real projective n-space fails to be a codimension n+1 fibrator, and certain manifolds covered by S3 fail to be codimension 4 fibrators.