Turk's head knots and links: A survey

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Di Prisa A., ŞAVK O.

Expositiones Mathematicae, cilt.44, sa.3, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.exmath.2026.125777
  • Dergi Adı: Expositiones Mathematicae
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Concordance properties, Hyperbolic structures, Knots and links: symmetries, Polynomial invariants
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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, non-split, prime, fibered, hyperbolic, invertible, and periodic. 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.