Right-angled Artin subgroups of Artin groups
Right-angled Artin subgroups of Artin groups
复制标题
Artin 群的直角 Artin 子群
DOI：
10.1112/jlms.12586
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Schreve, Kevin
中科院分区：
文献类型：
--
作者：
Jankiewicz, Kasia;Schreve, Kevin
由克里斯普和巴黎证明的山雀猜想指出，任何阿丁群的标准生成元的平方生成一个明显的直角阿丁子群。我们考虑由Artin群的不可约球面特殊子群的所有中心组成的更大的元素集，并猜想这些元素的足够大的幂产生一个明显的直角Artin子群。这个所谓的直角Artin子群在某种意义上是尽可能大的;它的神经与周围Artin群的神经同胚。我们对包含所有2$\hskip.001pt 2$-维Artin群的局部可约Artin群类和除E6，E7，E8$E_6，E_7，E_8$以外的任何类型的球面Artin群验证了这个猜想.我们用我们的结果得出结论，某些Artin组包含双曲曲面子群，回答问题的戈登，长和里德。
The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right‐angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the irreducible spherical special subgroups of the Artin group, and conjecture that sufficiently large powers of those elements generate an obvious right‐angled Artin subgroup. This alleged right‐angled Artin subgroup is in some sense as large as possible; its nerve is homeomorphic to the nerve of the ambient Artin group. We verify this conjecture for the class of locally reducible Artin groups, which includes all 2$\hskip.001pt 2$‐dimensional Artin groups, and for spherical Artin groups of any type other than E6,E7,E8$E_6, E_7, E_8$. We use our results to conclude that certain Artin groups contain hyperbolic surface subgroups, answering questions of Gordon, Long and Reid.