Signed ordered knotlike quandle presentations.
Nelson, Sam (2005)
Algebraic & Geometric Topology
Similarity:
Nelson, Sam (2005)
Algebraic & Geometric Topology
Similarity:
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.
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...
Isabel Darcy, De Sumners (1998)
Banach Center Publications
Similarity:
The following is an expository article meant to give a simplified introduction to applications of topology to DNA.
Vaughan Jones, Józef Przytycki (1998)
Banach Center Publications
Similarity:
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.
Mohnke, Klaus
Similarity:
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Vladimir Chernov, Rustam Sadykov (2016)
Fundamenta Mathematicae
Similarity:
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...
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.