Displaying similar documents to “Virtual Legendrian isotopy”

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.

Wirtinger presentations for higher dimensional manifold knots obtained from diagrams

Seiichi Kamada (2001)

Fundamenta Mathematicae

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A Wirtinger presentation of a knot group is obtained from a diagram of the knot. T. Yajima showed that for a 2-knot or a closed oriented surface embedded in the Euclidean 4-space, a Wirtinger presentation of the knot group is obtained from a diagram in an analogous way. J. S. Carter and M. Saito generalized the method to non-orientable surfaces in 4-space by cutting non-orientable sheets of their diagrams by some arcs. We give a modification to their method so that one does not need...

On slice knots in the complex projective plane.

Akira Yasuhara (1992)

Revista Matemática de la Universidad Complutense de Madrid

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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.

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.

Torus knots that cannot be untied by twisting.

Mohamed Ait Nouh, Akira Yasuhara (2001)

Revista Matemática Complutense

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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.

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.

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.