Homology n-spheres as codimension-(n+1) shape msimpl-fibrators

This paper identifies a class of homology n-spheres that are codimension-(n+1) shape msimpl-fibrators but are not shape msimpl-fibrators (a concept introduced by the author). Actually, the main result (Theorem 4.4) provides more general description of n-manifolds that are codimension-(k+1) shape msimpl-fibrators for 2⩽k⩽n. It establishes that any closed orientable PL n-manifold homotopically determined by π1, with Hopfian fundamental group and Hi(N)=0 for 0