Coperfectly Hopfian Groups and Shape Fibrator's Properties

Abstract

This paper provides further investigation of the concept of shape m${}_{\mathrm{simpl}}$-fibrators (previously introduced by the author). The main results identify shape m${}_{\mathrm{simpl}}$-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${}_{\mathrm{simpl}}$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${}_{\mathrm{simpl}}$o-fibrator, if it is a Hopfian manifold and a codimension-2 fibrator.

16 pages