论文标题
具有少数字符串的编织组的换向子亚组的同态
Homomorphisms of commutator subgroups of braid groups with small number of strings
论文作者
论文摘要
对于任何$ n $，我们描述了编织组$ b_n $及其换向器子组$ b'_n $的所有内态，以及所有同构$ b'_n \ to b_n $。这些结果仅针对小$ n $是新的，因为卡斯特尔已经用$ n \ ge 6 $描述了$ b_n $的内态性，而同构$ b'_n \ to b_n $和$ b'_n $的内态已被Kordek and Margalit的内态性描述为$ n \ n \ ge 7 $ 7 $。我们使用$ n = 4 $的方法非常不同，以及$ n \ ge 5 $。
For any $n$, we describe all endomorphisms of the braid group $B_n$ and of its commutator subgroup $B'_n$, as well as all homomorphisms $B'_n\to B_n$. These results are new only for small $n$ because endomorphisms of $B_n$ are already described by Castel for $n\ge 6$, and homomorphisms $B'_n\to B_n$ and endomorphisms of $B'_n$ are already described by Kordek and Margalit for $n\ge 7$. We use very different approaches for $n=4$ and for $n\ge 5$.
