论文标题
右角Artin内核同源的模块结构
Module structure of the homology of right-angled Artin kernels
论文作者
论文摘要
在本文中，我们研究了Artin内核同源的模块结构，即，非谐波字符的内核，从右角的Artin组到整数数字，模块的结构相对于ring $ \ Mathbb {k} [t^{\ pm 1}] $，其中$ \ mathbbbbbb {k} k {k} $是一个字段。 Papadima和Suciu通过Artin组图的标志复合物确定了该结构的某些部分。在这项工作中，我们提供了该模块的扭转部分的更多属性，例如，每个主要部分的尺寸和约旦形式的最大大小（如果我们用线性图来解释扭转结构）。这些特性是根据Flag复合物的合适过滤和相关的复合物的合适的双层覆盖物的同源性特性所陈述的。
In this paper, we study the module structure of the homology of Artin kernels, i.e., kernels of non-resonant characters from right-angled Artin groups onto the integer numbers, the module structure being with respect to the ring $\mathbb{K}[t^{\pm 1}]$, where $\mathbb{K}$ is a field of characteristic zero. Papadima and Suciu determined some part of this structure by means of the flag complex of the graph of the Artin group. In this work, we provide more properties of the torsion part of this module, e.g., the dimension of each primary part and the maximal size of Jordan forms (if we interpret the torsion structure in terms of a linear map). These properties are stated in terms of homology properties of suitable filtrations of the flag complex and suitable double covers of an associated toric complex.
