Displaying similar documents to “The colored Jones polynomials of the figure-eight knot and the volumes of three-manifolds obtained by Dehn surgeries”

Unknotting number and knot diagram.

Yasutaka Nakanishi (1996)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

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.

A Knot Polynomial Invariant for Analysis of Topology of RNA Stems and Protein Disulfide Bonds

Wei Tian, Xue Lei, Louis H. Kauffman, Jie Liang (2017)

Molecular Based Mathematical Biology

Similarity:

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...

Positive knots, closed braids and the Jones polynomial

Alexander Stoimenow (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

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...

Knots with property R + .

Clark, Bradd Evans (1983)

International Journal of Mathematics and Mathematical Sciences

Similarity:

On slice knots in the complex projective plane.

Akira Yasuhara (1992)

Revista Matemática de la Universidad Complutense de Madrid

Similarity:

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.