论文标题
紫红色群体的不可约生成的元素
Irreducible generating tuples of Fuchsian groups
论文作者
论文摘要
L. loder表明，表面组的任何产生元组都等同于稳定的标准产生元组，即$（a_1，\ ldots，a_k，a_k，1 \ ldots，1）$，其中$（a_1，\ ldots，a_k）$是标准生成元组。这尤其意味着不可约生的元素，即，nielsen的元素不等于形式的元组$（g_1，\ ldots，g_k，1）$，是最小的。在先前的作品中，第一授予者将大声的想法概括，并表明，所有不可还原且不可估计的生成足够大的fuchsian群体都可以由所谓的几乎是有刚性产生元组的几乎圆锥形的覆盖物来代表。 在本文中，\ cite {w2}的想法的变体用于表明，这种几乎具有刚性产生元组的几乎圆锥形覆盖物是独特的。此外，任何这种生成元组都是不可还原的。这提供了一种方法，可以展示许多尼尔森类别的非最小不可还原生成元素的类别。 作为一种应用，我们表明，与不可还原水平的Heegaard分裂相对应的Haken Seifert歧管基本组的元素是不可还原的。
L. Louder showed that any generating tuple of a surface group is Nielsen equivalent to a stabilized standard generating tuple i.e. $(a_1,\ldots ,a_k,1\ldots, 1)$ where $(a_1,\ldots ,a_k)$ is the standard generating tuple. This implies in particular that irreducible generating tuples, i.e. tuples that are not Nielsen equivalent to a tuple of the form $(g_1,\ldots ,g_k,1)$, are minimal. In a previous work the first author generalized Louder's ideas and showed that all irreducible and non-standard generating tuples of sufficiently large Fuchsian groups can be represented by so-called almost orbifold covers endowed with a rigid generating tuple. In the present paper a variation of the ideas from \cite{W2} is used to show that this almost orbifold cover with a rigid generating tuple is unique up to the appropriate equivalence. It is moreover shown that any such generating tuple is irreducible. This provides a way to exhibit many Nielsen classes of non-minimal irreducible generating tuples for Fuchsian groups. As an application we show that generating tuples of fundamental groups of Haken Seifert manifolds corresponding to irreducible horizontal Heegaard splittings are irreducible.
