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

Alan W. Reid; Shicheng Wang; Qing Zhou

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

Geometric Topology 2007-05-23 v1

Authors: Alan W. Reid , Shicheng Wang , Qing Zhou

Abstract

We address a conjecture that $\pi_1$ -surjective maps between closed aspherical 3-manifolds having the same rank on $\pi_1$ 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.

Keywords

hopfian property haken manifold 3-manifold groups simon's conjecture seifert manifolds epimorphisms

Cite

@article{arxiv.math/0002003,
  title  = {Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups},
  author = {Alan W. Reid and Shicheng Wang and Qing Zhou},
  journal= {arXiv preprint arXiv:math/0002003},
  year   = {2007}
}

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15 pages

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

Abstract

Keywords

Cite

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