Parabolic subgroups of two‐dimensional Artin groups and systolic‐by‐function complexes
Parabolic subgroups of two‐dimensional Artin groups and systolic‐by‐function complexes
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二维 Artin 群和收缩函数复合体的抛物线子群
DOI：
10.1112/blms.12697
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发表时间：
2021
影响因子：
0.9
通讯作者：
Martín Axel Blufstein
中科院分区：
文献类型：
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作者：
Martín Axel Blufstein
我们将Cumplido，Martin和Vasou以前关于大型Artin群的抛物子群的结果推广到更广泛的二维Artin群族。特别地，我们证明了(2，2)-Free二维Artin群的抛物子群的任意交本身就是抛物子群。一个Artin群是(2，2)-自由的，如果它的定义图没有两条由2标记的连续边。作为这一结果的结果，我们用Cumplido提出的算法解决了这一族的共轭稳定性问题。所有这一切都是通过考虑逐个功能的收缩复合体来实现的，它推广了收缩复合体。由于我们允许边缘具有不同的长度，因此按功能收缩的复合体具有比收缩复合体更灵活的结构。同时，它们的几何结构具有足够的刚性以满足类似于Cartan-Hadamard定理和其他类似于收缩复形的几何性质。
We extend previous results by Cumplido, Martin and Vaskou on parabolic subgroups of large‐type Artin groups to a broader family of two‐dimensional Artin groups. In particular, we prove that an arbitrary intersection of parabolic subgroups of a (2,2)‐free two‐dimensional Artin group is itself a parabolic subgroup. An Artin group is (2,2)‐free if its defining graph does not have two consecutive edges labeled by 2. As a consequence of this result, we solve the conjugacy stability problem for this family by applying an algorithm introduced by Cumplido. All of this is accomplished by considering systolic‐by‐function complexes, which generalize systolic complexes. Systolic‐by‐function complexes have a more flexible structure than systolic complexes since we allow the edges to have different lengths. At the same time, their geometry is rigid enough to satisfy an analogue of the Cartan–Hadamard theorem and other geometric properties similar to those of systolic complexes.