The nonuniqueness of Chekanov polynomials of Legendrian knots.
Melvin, Paul, Shrestha, Sumana (2005)
Geometry & Topology
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Displaying similar documents to “A Knot Polynomial Invariant for Analysis of Topology of RNA Stems and Protein Disulfide Bonds”
The nonuniqueness of Chekanov polynomials of Legendrian knots.
The colored Jones polynomials of the figure-eight knot and the volumes of three-manifolds obtained by Dehn surgeries
Hitoshi Murakami (2004)
Fundamenta Mathematicae
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I describe how the colored Jones polynomials of the figure-eight knot determine the volumes of the three-manifolds obtained by Dehn surgeries along it, according to my joint work with Y. Yokota.
Knot theory programs KNOT2000 (K2K) + LinKnot(K2K)+LinKnot(K2KC)
S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Minimizing the presentation of a knot group.
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Unknotting number and knot diagram.
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.
Mp-small summands increase knot width.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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A Family of Impossible Figures Studied by Knot Theory
Corinne Cerf (2002)
Visual Mathematics
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Applications of topology to DNA
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.
Unsolved problems in virtual knot theory and combinatorial knot theory
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.
On the first two Vassiliev invariants.
Willerton, Simon (2002)
Experimental Mathematics
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Lissajous knots and billiard knots
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.
The concordance genus of knots.
Livingston, Charles (2004)
Algebraic & Geometric Topology
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Spacefilling knots.
Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
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Virtual knot theory-unsolved problems
Roger Fenn, Louis H. Kauffman, Vassily O. Manturov (2005)
Fundamenta Mathematicae
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The present paper gives a quick survey of virtual and classical knot theory and presents a list of unsolved problems about virtual knots and links. These are all problems in low-dimensional topology with a special emphasis on virtual knots. In particular, we touch new approaches to knot invariants such as biquandles and Khovanov homology theory. Connections to other geometrical and combinatorial aspects are also discussed.
Every knot is a billiard knot
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.