Manifolds with hyperhopfian fundamental group as codimension-2 fibrators

Every hopfian n-manifold N with hyperhopfian fundamental group is known to be a codimension-2 orientable fibrator. In this paper, we generalize to the non-orientable setting by considering the covering space (N) over tilde of N corresponding to H, where II is the intersection of all subgroups H-i of index 2 in nl (N). First, we will show that if pi(1) (N) is hyperhopfian and (N) over tilde is hopfian, then N is a codimension-2 fibrator. Then we get several results about codimension-2 fibrators as corollaries. (C) 1999 Elsevier Science B.V. All rights reserved. AMS classification: Primary 57N15; 55R65, Secondary 57N25; 54B15.