The slicing number of a knot.
Livingston, Charles (2002)
Algebraic & Geometric Topology
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Livingston, Charles (2002)
Algebraic & Geometric Topology
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Motegi, Kimihiko, Song, Hyun-Jong (2005)
Algebraic & Geometric Topology
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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.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Seiichi Kamada (2001)
Fundamenta Mathematicae
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A Wirtinger presentation of a knot group is obtained from a diagram of the knot. T. Yajima showed that for a 2-knot or a closed oriented surface embedded in the Euclidean 4-space, a Wirtinger presentation of the knot group is obtained from a diagram in an analogous way. J. S. Carter and M. Saito generalized the method to non-orientable surfaces in 4-space by cutting non-orientable sheets of their diagrams by some arcs. We give a modification to their method so that one does not need...
Clark, Bradd Evans (1983)
International Journal of Mathematics and Mathematical Sciences
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Mulazzani, Michele (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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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.
S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Akira Yasuhara (1992)
Revista Matemática de la Universidad Complutense de Madrid
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We investigate the knots in the boundary of the punctured complex projective plane. Our result gives an affirmative answer to a question raised by Suzuki. As an application, we answer to a question by Mathieu.
Ying-Qing Wu (1993)
Mathematische Annalen
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