Turk’s head knots and links: A survey

We collect and discuss various results on an important family of knots and links called Turk’s head knots and links . 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, the Turk’s head links are all known to be alternating, non-split, prime, fibered, hyperbolic, invertible, and periodic. The Turk’s head links are also both positive and negative amphichiral if it is chosen to be odd. Moreover, we highlight and present several more results, focusing on Turk’s head knots on 3 strands. 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