Displaying similar documents to “A Knot Polynomial Invariant for Analysis of Topology of RNA Stems and Protein Disulfide Bonds”

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.

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.

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.

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.