The nonuniqueness of Chekanov polynomials of Legendrian knots.
Melvin, Paul, Shrestha, Sumana (2005)
Geometry & Topology
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Melvin, Paul, Shrestha, Sumana (2005)
Geometry & Topology
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Livingston, Charles (2002)
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.
Wei Tian, Xue Lei, Louis H. Kauffman, Jie Liang (2017)
Molecular Based Mathematical Biology
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Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are not taken into account in conventional knot polynomials. In this study, we develop a new class...
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...
Plamenevskaya, Olga (2004)
Algebraic & Geometric Topology
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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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Livingston, Charles (2004)
Algebraic & Geometric Topology
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Clark, Bradd Evans (1983)
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.
Willerton, Simon (2002)
Experimental Mathematics
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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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.