Minimizing the presentation of a knot group.
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Yasutaka Nakanishi (1996)
Revista Matemática de la Universidad Complutense de Madrid
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This note is a continuation of a former paper, where we have discussed the unknotting number of knots with respect to knot diagrams. We will show that for every minimum-crossing knot-diagram among all unknotting-number-one two-bridge knot there exist crossings whose exchange yields the trivial knot, if the third Tait conjecture is true.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Nafaa Chbili (2003)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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.
Livingston, Charles (2003)
Geometry & Topology
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Corinne Cerf (2002)
Visual Mathematics
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Mulazzani, Michele (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Vaughan Jones, Józef Przytycki (1998)
Banach Center Publications
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We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.