Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups

Reid, Alan W.; Wang, Shicheng; Zhou, Qing

Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups

Authors

Reid, Alan W.

Wang, Shicheng

Zhou, Qing

Description

We address a conjecture that $π_1$-surjective maps between closed aspherical 3-manifolds having the same rank on $π_1$ must be of non-zero degree. The conjecture is proved for Seifert manifolds, which is used in constructing the first known example of minimum Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3-manifolds.
15 pages