Turk's-head Knots (Braided Band Knots) a Mathematical Modeling
Skip Pennock (2005)
Visual Mathematics
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Skip Pennock (2005)
Visual Mathematics
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Mulazzani, Michele (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Skip Pennock (2004)
Visual Mathematics
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Kuniaki Horie, Mitsuko Horie (2003)
Acta Arithmetica
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Dennis Roseman (1975)
Fundamenta Mathematicae
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Kai Ishihara, Atsushi Ishii (2012)
Fundamenta Mathematicae
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A handlebody-knot is a handlebody embedded in the 3-sphere. We improve Luo's result about markings on a surface, and show that an IH-move is sufficient to investigate handlebody-knots with spatial trivalent graphs without cut-edges. We also give fundamental moves with a height function for handlebody-tangles, which helps us to define operator invariants for handlebody-knots. By using the fundamental moves, we give an operator invariant.
Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
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Richard Hartley (1980)
Mathematische Zeitschrift
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C.McA. Gordon (1981)
Mathematische Annalen
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Mohamed Ait Nouh, Akira Yasuhara (2001)
Revista Matemática Complutense
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We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.
Motegi, Kimihiko, Song, Hyun-Jong (2005)
Algebraic & Geometric Topology
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Willerton, Simon (2002)
Experimental Mathematics
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P. V. Koseleff, D. Pecker (2014)
Banach Center Publications
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We show that every knot can be realized as a billiard trajectory in a convex prism. This proves a conjecture of Jones and Przytycki.