Generalized Hopfian Property,a Minimal Haken Manifold,and Epimorphisms Between 3-Manifold Groups |
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| Authors: | Alan?W.?Reid mailto:areid@antfire.ma.utexa.edu" title=" areid@antfire.ma.utexa.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Shi?Cheng?Wang,Qing?Zhou |
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| Affiliation: | (1) Department of Mathematics, University of Texas, Austin, TX 78712, USA E-mail: areid@antfire.ma.utexa.edu, US;(2) Department of Mathematics, Peking University, Beijing 100871, P. R. China E-mail: swang@sxxO.math.pku.edu.cn, CN;(3) Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China E-mail: qzhou@math.ecnu.edu.cn, CN |
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| Abstract: | ![]()
We address the question that if π1-surjective maps between closed aspherical 3-manifolds have the same rank on π1 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. Received September 16, 1999, Revised August 31, 2000, Accepted March 29, 2001. |
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| Keywords: | Non-zero degree maps Epimorphisms 3-Manifolds |
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