Connected sums of manifolds which induce approximate fibrations

Codimension-2 fibrators are n-manifolds which automatically induce approximate fibration, in the following sense: given any proper mapping p from an (n + 2)-manifold onto a 2-manifold such that each point-preimage is a copy of the codimension-2 fibrator, p is necessarily an approximate fibration. In this paper, we give some answers to the following question: given an n-manifold N which is a nontrivial connected sum, when is N a codimension-2 fibrator?.