论文标题
在三链单数辫子组的某些分解中
On some decompositions of the 3-strand Singular Braid Group
论文作者
论文摘要
令$ sb_n $为辫子生成器$σ_i$和单数编织生成器$τ_i$，$ 1 \ leq i \ leq n-1 $生成的单数编织组。令$ st_n $表示同构的内核，该组映射，每$ i $，$σ_i$ to Cyclic置换$（i，i，i+1）$和$τ_i$ to $ 1 $。在本文中，我们调查了组$ ST_3 $。我们获得了$ ST_3 $的演示文稿。我们证明，$ ST_3 $对$ 3 $ strands的单数纯编织组$ sp_3 $是同构。我们还证明，$ st_3 $是亚组$ h $和无限环保组的半主导产品，其中子组$ h $是$ {\ mathbb z}^2 \ ast {\ ast {\ mathbb z}^2 $的$ {\ mathbb z}^2 \ ast的Hnn-Extension。
Let $SB_n$ be the singular braid group generated by braid generators $σ_i$ and singular braid generators $τ_i$, $1 \leq i \leq n-1$. Let $ST_n$ denote the group that is the kernel of the homomorphism that maps, for each $i$, $σ_i$ to the cyclic permutation $(i, i+1)$ and $τ_i$ to $1$. In this paper we investigate the group $ST_3$. We obtain a presentation for $ST_3$. We prove that $ST_3$ is isomorphic to the singular pure braid group $SP_3$ on $3$ strands. We also prove that the group $ST_3$ is semi-direct product of a subgroup $H$ and an infinite cyclic group, where the subgroup $H$ is an HNN-extension of ${\mathbb Z}^2 \ast {\mathbb Z}^2$.
