Generalized Hopfian Property, a Minimal Haken Manifold, and Epimorphisms Between 3-Manifold Groups
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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.
KeywordsNon-zero degree maps Epimorphisms 3-Manifolds
MR (2000) Subject Classification55N05 57M05 57N10
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