论文标题
大型Artin组的同构问题
The isomorphism problem for large-type Artin groups
论文作者
论文摘要
在本文中，我们解决了所有大型Artin组的同构问题。我们的策略涉及以纯粹的代数方式重建与大型Artin组相关的Coxeter组。这回答了Charney提出的几个问题。 我们还一般研究二维Artin组。通过对其所有二面体ARTIN亚组进行分类，我们能够为所有二维Artin组提供强大的刚性结果。我们证明，二维ARTIN组中的“大多数”标准发电机在同构（结合）下保存下来。我们还表明，大型Artin组之间的同构可保留球形抛物线亚组的集合，并且仅当定义图没有均匀的叶子时。最后，我们表明，其定义图的Artin群体均匀标记的叶子从来都不是共同的。
In this paper we solve the isomorphism problem for all large-type Artin groups. Our strategy involves reconstructing the Coxeter groups associated with large-type Artin groups in a purely algebraic way. This answers several questions raised by Charney. We also study 2-dimensional Artin groups in general. By classifying all their dihedral Artin subgroups, we are able to give strong results of rigidity for all 2-dimensional Artin groups. We prove that "most" standard generators in 2-dimensional Artin groups are preserved under isomorphisms (up to conjugation). We also show that an isomorphism between large-type Artin groups preserves the set of spherical parabolic subgroups if and only if the defining graphs do not have even-labelled leaves. Finally, we show that Artin groups whose defining graphs have even-labelled leaves are never co-Hopfian.
