### Ribbon Concordance of Knots in the 3-Sphere.

C.McA. Gordon (1981)

Mathematische Annalen

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C.McA. Gordon (1981)

Mathematische Annalen

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J.A. Hillman, S.P. Plotnick (1990)

Mathematische Annalen

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Makoto Sakuma, Kanji Morimoto (1991)

Mathematische Annalen

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S. Jablan, R. Sazdanovic (2003)

Visual Mathematics

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Hendricks, Jacob (2004)

Algebraic & Geometric Topology

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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.

Ronald Fintushel, Ronald J. Stern (1980)

Mathematische Zeitschrift

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C. McA. Gordon, José María Montesinos (1986)

Mathematische Annalen

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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.

Schmitt, Peter (1997)

Beiträge zur Algebra und Geometrie

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Mulazzani, Michele (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Daniel S. Silver (1993)

Mathematische Annalen

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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.

Vladimir Chernov, Rustam Sadykov (2016)

Fundamenta Mathematicae

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An elementary stabilization of a Legendrian knot L in the spherical cotangent bundle ST*M of a surface M is a surgery that results in attaching a handle to M along two discs away from the image in M of the projection of the knot L. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies. A class of virtual Legendrian isotopy is called a virtual Legendrian knot. In contrast to Legendrian knots, virtual Legendrian knots...