On simple fibered knots in S5 and the existence of decomposable algebraic 3-knots.
Osamu Saeki (1987)
Commentarii mathematici Helvetici
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Osamu Saeki (1987)
Commentarii mathematici Helvetici
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J.M. Montesinos, F. González-Acuna (1983)
Commentarii mathematici Helvetici
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S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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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.
Alan W. Reid, Colin C. Adams (1996)
Commentarii mathematici Helvetici
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Corinne Cerf (2002)
Visual Mathematics
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Patrick Gilmer (1993)
Commentarii mathematici Helvetici
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Roger Fenn, Denis P. Ilyutko, Louis H. Kauffman, Vassily O. Manturov (2014)
Banach Center Publications
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This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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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.
Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
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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.