Minimizing the presentation of a knot group.
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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.
S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
Similarity:
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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...
Livingston, Charles (2004)
Geometry & Topology
Similarity:
Roger Fenn, Denis P. Ilyutko, Louis H. Kauffman, Vassily O. Manturov (2014)
Banach Center Publications
Similarity:
This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.
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.
Ying-Qing Wu (1993)
Mathematische Annalen
Similarity:
Corinne Cerf (2002)
Visual Mathematics
Similarity:
Mohamed Ait Nouh, Akira Yasuhara (2001)
Revista Matemática Complutense
Similarity:
We give a necessary condition for a torus knot to be untied by a single twisting. By using this result, we give infinitely many torus knots that cannot be untied by a single twisting.
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.
Clark, Bradd Evans (1983)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
Similarity: