Acta Mathematica Sinica

, Volume 18, Issue 1, pp 157–172 | Cite as

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

  • Alan W. ReidEmail author
  • Shi Cheng Wang
  • Qing Zhou


We address the question that if π 1-surjective maps between closed aspherical 3-manifolds have the same rank on π 1 they must be of non-zero degree. The positive answer is proved for Seifert manifolds, which is used in constructing the first known example of minimal Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3-manifolds. Many examples are given.


Non-zero degree maps Epimorphisms 3-Manifolds 

MR (2000) Subject Classification

55N05 57M05 57N10 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TexasAustinUSA
  2. 2.Department of MathematicsPeking UniversityBeijingP. R. China
  3. 3.Department of MathematicsEast China Normal UniversityShanghaiP. R. China

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