The Action Dimension of Artin Groups
The Action Dimension of Artin Groups
复制标题
Artin团体的行动维度
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Mike Davis Fields
中科院分区：
文献类型：
--
作者：
Mike Davis Fields
离散群G的作用维数是可收缩流形的最小维数，它允许一个真G-作用。本文研究了一般Artin群的作用维数。主要结果是：如果Artin群满足K（π，1）-猜想，且神经L的Z-系数上同调群是平凡的，则神经L的维数为n（n6 = 2）的Artin群的作用维数小于或等于（2n+1）.当n = 2时，我们还需要一个关于L的条件来得到同样的不等式，即L的基本群是由r个元素生成的，其中r是H1（L，Z）的秩。我们通过构造一个以Artin群为基本群的2n + 1维非球面流形来证明我们的定理。AMS分类编号。初级：20 F36、20 F65次级：32 S22
The action dimension of a discrete group G is the minimum dimension of a contractible manifold, which admits a proper G-action. In this dissertation, we study the action dimension of general Artin groups. The main result is that the action dimension of an Artin group with the nerve L of dimension n for n 6= 2 is less than or equal to (2n+1) if the Artin group satisfies the K(π, 1)-Conjecture and the top cohomology group of L with Z-coefficients is trivial. For n = 2, we need one more condition on L to get the same inequality; that is the fundamental group of L is generated by r elements where r is the rank of H1(L,Z). We prove our theorem by constructing an aspherical manifold of dimension 2n + 1 which has the Artin group as its fundamental group. AMS classification numbers. Primary: 20F36, 20F65 Secondary: 32S22