论文标题
编织组$ b_3 $在持续分数的框架中
The braid group $B_3$ in the framework of continued fractions
论文作者
论文摘要
我们将编织组$ b_3 $的经典解释用作模块化组$ \ text {psl} _2 \ left（\ mathbb {z} \ right）$的中心扩展，以建立$ b_3 $的新的和基本属性的$。特别是，我们提供了简单而自然的线性时间算法，以解决$ b_3 $中的单词和共轭问题。本文介绍的算法易于实现，并且是文献中最有效的算法，可以在编织组$ b_3 $中解决这些问题。
We use the classical interpretation of the braid group $B_3$ as a central extension of the modular group $\text{PSL}_2\left(\mathbb{Z}\right)$ to establish new and fundamental properties of $B_3$ using the theory of continued fractions. In particular, we give simple and natural linear time algorithms to solve the word and conjugacy problems in $B_3$. The algorithms introduced in this paper are easy to implement and are the most efficient algorithms in the literature to solve these problems in the braid group $B_3$.
