论文标题
Artin团体的右角Artin子组
Right-angled Artin subgroups of Artin groups
论文作者
论文摘要
山雀的猜想是由Crisp和Paris证明的，指出任何Artin组的标准发电机的正方形都会产生一个明显的右角Artin子组。我们考虑了一组较大的元素，该元素由Artin组的所有不可还原的球形特殊子组组成，并猜想这些元素足够大的功率产生了明显的右角Artin子组。从某种意义上说，这个所谓的右角Artin子组是尽可能大的。它的神经对环境Artin组的神经是同构的。我们为本地还原的Artin组验证了这一猜想，其中包括所有$ 2 $维的Artin组，以及除$ e_6 $，$ e_7 $，$ e_8 $以外的任何类型的球形Artin组。我们使用我们的结果来得出结论，某些ARTIN组包含双曲线表面亚组，回答了戈登（Gordon），朗和里德（Reid）的问题。
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 $2$-dimensional Artin groups, and for spherical Artin groups of any type other than $E_6$, $E_7$, $E_8$. We use our results to conclude that certain Artin groups contain hyperbolic surface subgroups, answering questions of Gordon, Long and Reid.
