Homology n-spheres as codimension- 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 π 1 , with Hopfian fundamental group and H i ( N ) = 0 for 0 < i < k ⩽ n , where k ⩾ 2 , is a codimension- ( k + 1 ) shape msimpl-fibrator.