Nielsen number is a knot invariant
Alexander Fel'shtyn (2007)
Banach Center Publications
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We show that the Nielsen number is a knot invariant via representation variety.
Alexander Fel'shtyn (2007)
Banach Center Publications
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We show that the Nielsen number is a knot invariant via representation variety.
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...
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Roger Fenn, Denis P. Ilyutko, Louis H. Kauffman, Vassily O. Manturov (2014)
Banach Center Publications
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This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.
S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Etnyre, John B. (1999)
Geometry & 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.
Corinne Cerf (2002)
Visual Mathematics
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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.
Willerton, Simon (2002)
Experimental Mathematics
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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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...