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 x S-k onto itself such that proj h : N x (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 S-3 fail to be codimension 4 fibrators. (C) 1999 Published by Elsevier Science B.V. All rights reserved.