图克头结和链接：综述
Turk's head knots and links: a survey
AI总结：
本文综述了图克头结和链接的性质，讨论了其数学特性及开放问题。
摘要：
我们收集并讨论了被称为图克头结和链接$Th (p,q)$的重要结和链接家族的各种结果。在数学文献中，它们也以不同的名称出现，如玫瑰结和链接或编织结和链接。除非是无结或交替扭结$T(2,q)$，图克头链接$Th (p,q)$都被已知为交替的、纤维化的、双曲的、可逆的、非分裂的、周期性的和素的。图克头链接$Th (p,q)$如果$p$被选择为奇数，则既是正的又是负的镜像对称的。此外，我们强调并呈现了几个更多的结果，重点是图克头结$Th (3,q)$。我们最后列出了图克头结和链接的一些开放问题和猜想。我们最后附上关于扭结和链接的简短附录，这可能具有独立的兴趣。
英文摘要：
We collect and discuss various results on an important family of knots and links called Turk's head knots and links $Th (p,q)$. In the mathematical literature, they also appear under different names such as rosette knots and links or weaving knots and links. Unless being the unknot or the alternating torus links $T(2,q)$, the Turk's head links $Th (p,q)$ are all known to be alternating, fibered, hyperbolic, invertible, non-split, periodic, and prime. The Turk's head links $Th (p,q)$ are also both positive and negative amphichiral if $p$ is chosen to be odd. Moreover, we highlight and present several more results, focusing on Turk's head knots $Th (3,q)$. We finally list several open problems and conjectures for Turk's head knots and links. We conclude with a short appendix on torus knots and links, which might be of independent interest.
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。
