Manifolds with finite cyclic fundamental groups and codimension 2 fibrators

A closed connected n-manifold N is called a codimension 2 fibrator (codimension 2 orientable fibrator, respectively) if each proper map p : M --> B on an (orientable, respectively) (n + 2)-manifold M each fiber of which is shape equivalent to N is an approximate fibration. Let r be a nonnegative integer and let N be a closed n-manifold whose fundamental group is isomorphic to H-1 x H-2, where H-1 is a group whose order is odd and H-2 is a finite direct product of cyclic groups of order 2(r). Let q(1) : N-1 --> N be the covering associated with H-1. The main purpose of this paper shows that if N-1 is a codimension 2 orientable fibrator, then N is a codimension 2 fibrator. (C) 2000 Elsevier Science B.V. All rights reserved.