Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups
Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups
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广义 Hopfian 性质、最小 Haken 流形以及 3 流形群的 J. Simon 猜想
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Qing Zhou
中科院分区：
文献类型：
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作者：
A. Reid;Shicheng Wang;Qing Zhou
本文提出了一个猜想：在$\pi_1$上具有相同秩的闭非球面3-流形之间的$\pi_1$-满射一定是非零度的.证明了Seifert流形上的猜想，并利用该猜想构造了已知的第一个极小Haken流形的例子。另一个动机是通过3-流形之间的非零度映射来研究3-流形群的满态。
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.