Generalized Hopfian Property, a Minimal Haken Manifold, and Epimorphisms Between 3-Manifold Groups

摘要

We address the question that if π1-surjective maps between closed aspherical 3-manifoldshave the same rank on π1 they must be of non-zero degree. The positive answer is proved for Seifertmanifolds, which is used in constructing the first known example of minimal Haken manifold. Anothermotivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3-manifolds. Many examples are given.