Coperfectly Hopfian groups and shape fibrator's properties

摘要

This paper provides further investigation of the concept of shape m(simpl)-fibrators (previously introduced by the author). The main results identify shape m(simpl)-fibrators among direct products of Hopfian manifolds. First it is established that every closed orientable manifold homotopically determined by pi(1) with coperfectly Hopfian group (a new class of Hopfian groups that are introduced here) is a shape m(simpl)o-fibrator if it is a codimension-2 fibrator (Theorem 5.4). The main result (Theorem 6.2) states that the direct product of two closed orientable manifolds (of different dimension) homotopically determined by pi(1) and with coperfectly Hopfian fundamental groups (one normally incommensurable with the other one) is a shape m(simpl)o-fibrator, if it is a Hopfian manifold and a codimension-2 fibrator. (C) 2019 Elsevier B.V. All rights reserved.