Maps from 3-manifolds to 4-manifolds that induce isomorphisms on π1

Abstract

In this paper, we prove that if a closed orientable [Formula: see text]-manifold [Formula: see text] admits a map [Formula: see text] to a closed orientable [Formula: see text]-manifold [Formula: see text] such that [Formula: see text] induces an isomorphism on fundamental groups, then [Formula: see text] is homeomorphic to [Formula: see text] or [Formula: see text]. Relevant results on higher dimensional manifolds are also obtained.