论文标题
关于Breidze和Traczyk对Burau代表的忠诚的考虑，以$ n = 4 $
On the considerations adopted by Breidze and Traczyk towards the faithfulness of Burau representation for $n=4$
论文作者
论文摘要
这项工作讨论了减少Burau代表的忠实问题的开放问题，价格为$ n = 4 $。伯曼（Birman）表明，为了证明这种表示是忠实的，足以找到两个矩阵$ a $ a $ a $ a和$ b $产生免费等级的免费组。Breidze和Traczyk证明了$ a^{3} $和$ b^{3} $ a^$ after的$ a^$ a $ a $ a^2} 2。
This work discusses the open problem of the faithfulness of the reduced Burau representation for $n=4$. Birman showed that in order to prove this representation is faithful, it is sufficient to find two matrices $A$ and $B$ that generate a free group of rank 2. Breidze and Traczyk proved that $A^{3}$ and $B^{3}$ generate the free group of rank 2. In our work, we show that $A^{2}$ and $B^{2}$ generate the free group of rank 2.
