Signed ordered knotlike quandle presentations.
Nelson, Sam (2005)
Algebraic & Geometric Topology
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Nelson, Sam (2005)
Algebraic & Geometric Topology
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Józef Przytycki (1998)
Banach Center Publications
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Paweł Traczyk (1995)
Banach Center Publications
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Alexander Stoimenow (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Using the recent Gauß diagram formulas for Vassiliev invariants of Polyak-Viro-Fiedler and combining these formulas with the Bennequin inequality, we prove several inequalities for positive knots relating their Vassiliev invariants, genus and degrees of the Jones polynomial. As a consequence, we prove that for any of the polynomials of Alexander/Conway, Jones, HOMFLY, Brandt-Lickorish-Millett-Ho and Kauffman there are only finitely many positive knots with the same polynomial and no...
Isabel Darcy, De Sumners (1998)
Banach Center Publications
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The following is an expository article meant to give a simplified introduction to applications of topology to DNA.
Greene, Michael, Wiest, Bert (1998)
Geometry & Topology
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Ekholm, Tobias, Wolff, Maxime (2002)
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.
Ng, Lenhard L. (2001)
Algebraic & Geometric Topology
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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.