论文标题
$ 3 $ - 可加油的汤普森组和链接的三色性
The $3$-colorable subgroup of Thompson's group and tricolorability of links
论文作者
论文摘要
从琼斯（Jones）在汤普森（Thompson）组$ f $的代表作品中的工作开始，已经定义和研究了带有有趣属性的$ f $的子组。这些子组之一称为$ 3 $ - 颜色的亚组$ \ mathcal {f} $，该{f} $由其树图给出的``区域''的元素组成。另一方面，琼斯在代表作品中还提供了一种构建$ f $元素的结和链接的方法。因此，探索$ \ Mathcal {f} $中的元素与$ 3 $ - 可加油的链接之间的元素之间的关系是一个自然的问题。在本文中，我们显示$ \ Mathcal {f} $中的所有元素都给出3色链接。
Starting from the work by Jones on representations of Thompson's group $F$, subgroups of $F$ with interesting properties have been defined and studied. One of these subgroups is called the $3$-colorable subgroup $\mathcal{F}$, which consists of elements whose ``regions'' given by their tree diagrams are $3$-colorable. On the other hand, in his work on representations, Jones also gave a method to construct knots and links from elements of $F$. Therefore it is a natural question to explore a relationship between elements in $\mathcal{F}$ and $3$-colorable links in the sense of knot theory. In this paper, we show that all elements in $\mathcal{F}$ give 3-colorable links.
