论文标题
关于编织组的一致性亚组的商
On quotients of congruence subgroups of braid groups
论文作者
论文摘要
整体burau表示将编织组的地图分为一组整体矩阵。这允许将编织组的一致性子组定义为整体矩阵通常的主要一致性亚组的预先形象。我们通过检查级别可分裂性引起的系列中可能出现的一些商来探索这些一致性亚组的结构。我们基于Stylianakis对一致性子组的对称商的工作，该组本身概括了纯编织组的编织组的商。我们通过利用纽曼在整体矩阵上的结果并在任何换位的预先映射中明确查找元素来实现这一目标。通过避免将生成集用于一致性亚组，使我们的概括成为可能。我们根据布伦德尔（Brendle）和玛格丽特（Margalit）的结果以及科德克（Kordek）和玛格丽特（Margalit）在第四级一致性亚组中发现了进一步的概括。这为对称群体不是同构的商家族提供了。
The integral Burau representation provides a map from the braid group into a group of integral matrices. This allows for a definition of congruence subgroups of the braid group as the preimage of the usual principal congruence subgroups of integral matrices. We explore the structure these congruence subgroups by examining some of the quotients that may arise in the series induced by divisibility of levels. We build on the work of Stylianakis on symmetric quotients of congruence subgroups, which itself generalizes the quotient of the braid group by the pure braid group. We accomplish this by utilizing results of Newman on integral matrices and explicitly finding elements in the preimage of any transposition. Our generalization is made possible by avoiding the use of a generating set for congruence subgroups. We find further generalizations based on results of Brendle and Margalit as well as Kordek and Margalit on the level four congruence subgroup. This gives families of quotients which are not isomorphic to symmetric groups.
