Displaying similar documents to “Reidemeister-type moves for surfaces in four-dimensional space”

Twisting and unknotting operations.

Yoshiyuki Ohyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

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We define a twisting move, an (n,k)-move, on a link diagram and consider the question as to whether or not any two links are equivalent by this move. Moreover we show that any knot can be trivialized by at most twice twisting operations.

Arc presentations of knots and links

Peter Cromwell (1998)

Banach Center Publications

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s paper presents some examples and a survey of results concerning a new way of presenting knots and links, together with the corresponding link invariant. More detailed accounts are given in [Cr, C-N, Nu1, Nu2, Nu3].

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.

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.