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 Ñ of N corresponding to H, where H is the intersection of all subgroups Hi of index 2 in π1(N). First, we will show that if π1(N) is hyperhopfian and Ñ is hopfian, then N is a codimension-2 fibrator. Then we get several results about codimension-2 fibrators as corollaries.