Nielsen equivalence in fuchsian groups and seifert fibered spaces
Nielsen equivalence in fuchsian groups and seifert fibered spaces
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fuchsian 群和 Seifert 纤维空间中的 Nielsen 等价
DOI：
10.1016/0040-9383(91)90005-o
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
Y. Moriah
中科院分区：
文献类型：
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作者：
M. Lustig;Y. Moriah
本文研究了Seifert三维流形M的Heegaard分裂Z及其下标Fuchsian群G的生成系统，引入并计算了一个数值不变量I4*(I；)W+.哪一个。在M的例外纤维具有奇数且相对素数的情况下，完全分类了最小亏格的“垂直”Hcegaard分裂。尤其是。T-(Z)区分了Seifert纤维同调球面的最小亏格“垂直”Hcegaard分裂。不变量。B‘(I：)是由一个取值在58’中的数值不变量描述的，它证明了Niclscn等价(XC定义1.1)生成G的最小基数系统WC证明：
IN THIS paper we investigate Heegaard splittings Z of Seifert fibered 3-manifolds M and generating systems for the underlying Fuchsian groups G. We introduce and compute a numerical invariant i4*(I;)~ W+. which. in the case where the exceptional fibers of M have odd and relatively prime multiplicities, completely classifies “vertical” Hcegaard splittings of minimal genus. In particular. t-(Z) distinguishes between minimal genus “vertical” Hcegaard splittings of Seifert fibered homology spheres. The invariant. b ‘(I:) is dcrivcd from a numerical invariant with values in 58’which exhibits Niclscn incquivalent (XC Dchnition 1.1) gcncrating systems of minimal cardinality for G. WC prove: