论文标题
千古的辫子，奇异的链接和漫画类型的亚组
Singular braids, singular links and subgroups of camomile type
论文作者
论文摘要
在本文中，我们找到了一组有限的发电机和奇异纯编织组$ sp_n $，$ n \ geq 3 $的定义关系，这是单数编织组$ sg_n $的子组。使用此演示文稿，我们证明了$ sg_n $的中心（等于$ n \ geq 3 $的$ sp_n $中心）是$ sp_n $的直接因素，但它不是$ sp_n $的直接因素。我们介绍了Commile类型的子组，并证明了单数纯编织组$ sp_n $，$ n \ geq 5 $，是$ sg_n $中的commile类型的子组。另外，我们还使用自由古德尔（Guandle）的内态构造单数单型单体的代表来构建基本的单Quandle。对于任何单数链接，我们定义了一些群体家庭，这些群体是此链接的不变。
In this paper we find a finite set of generators and defining relations for the singular pure braid group $SP_n$, $n \geq 3$, that is a subgroup of the singular braid group $SG_n$. Using this presentation, we prove that the center of $SG_n$ (which is equal to the center of $SP_n$ for $n \geq 3$) is a direct factor in $SP_n$ but it is not a direct factor in $SP_n$. We introduce subgroups of camomile type and prove that the singular pure braid group $SP_n$, $n \geq 5$, is a subgroup of camomile type in $SG_n$. Also we construct the fundamental singquandle using a representation of the singular braid monoid by endomorphisms of free guandle. For any singular link we define some family of groups which are invariants of this link.
