Determining the action dimension of an Artin group by using its complex of abelian subgroups
Determining the action dimension of an Artin group by using its complex of abelian subgroups
复制标题
利用阿贝尔子群的复形确定 Artin 群的作用维数
DOI：
10.1112/blms.12061
复制
发表时间：
2016
影响因子：
0.9
通讯作者：
Jingyin Huang
中科院分区：
文献类型：
--
作者：
Michael W. Davis;Jingyin Huang
设（W，S）是一个Coxeter系统，其关联的Artin群为A，神经为单纯复形L.我们在A中定义了“标准交换子群”的概念。A中这类子群的偏序集由L的某个细分L的单形的偏序集参数化。这个标准交换子群的复形被用来将一个早期的结果从直角Artin群的情况推广到一般Artin群的情况，在许多情况下，通过计算BA的流形模型的最小维数。(This是A的“动作维度”，表示为actdimA。）如果Hd（L;Z/2）≥ 0，其中d=dimL，则actdimA ≥ 2d+2。此外，当K（π，1）-猜想对A成立时，不等式是等式。
Suppose that (W,S) is a Coxeter system with associated Artin group A and with a simplicial complex L as its nerve. We define the notion of a ‘standard abelian subgroup’ in A . The poset of such subgroups in A is parameterized by the poset of simplices in a certain subdivision L⊘ of L . This complex of standard abelian subgroups is used to generalize an earlier result from the case of right‐angled Artin groups to case of general Artin groups, by calculating, in many instances, the smallest dimension of a manifold model for BA . (This is the ‘action dimension’ of A denoted actdimA .) If Hd(L;Z/2)≠0 , where d=dimL , then actdimA⩾2d+2 . Moreover, when the K(π,1) ‐Conjecture holds for A , the inequality is an equality.