Thompson群中链图的正则同位素类
Regular Isotopy Classes of Link Diagrams From Thompson's Groups
摘要：
2014年，Vaughan Jones开发了一种方法来从Thompson群$F$的元素中产生链接，并表明所有链接都是这样产生的。他还介绍了一个小组$\vec{F}$的$F$和一种方法，以产生定向链接的元素，这一小组。在2018年，Valeriano Aiello证明了所有有向链接都来自这种构造。我们对$F$产生的那些正则合痕类链路进行了精确分类，以及对$\vec{F}$产生的那些定向链路的正则合痕类链路进行了精确分类，回答了Jones在2018年提出的一个问题。
英文摘要：
In 2014, Vaughan Jones developed a method to produce links from elements of Thompson's group $F$, and showed that all links arise this way. He also introduced a subgroup $\vec{F}$ of $F$ and a method to produce oriented links from elements of this subgroup. In 2018, Valeriano Aiello showed that all oriented links arise from this construction. We classify exactly those regular isotopy classes of links that arise from $F$, as well as exactly those regular isotopy classes of oriented links that arise from $\vec{F}$, answering a question asked by Jones in 2018.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
