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

Alan W. Reid; Shi Cheng Wang; Qing Zhou

doi:10.1007/s101140100141

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

Alan W. Reid^*
, Shi Cheng Wang
, Qing Zhou

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	157-172
Number of pages	16
Journal	Acta Mathematica Sinica, English Series
Volume	18
Issue number	1
DOIs	https://doi.org/10.1007/s101140100141
State	Published - Jan 2002

Keywords

3-Manifolds
Epimorphisms
Non-zero degree maps

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10.1007/s101140100141

Cite this

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AB - 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.

KW - 3-Manifolds

KW - Epimorphisms

KW - Non-zero degree maps

UR - https://www.scopus.com/pages/publications/0344771498

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

Abstract

Keywords

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