The slicing number of a knot.
Livingston, Charles (2002)
Algebraic & Geometric Topology
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Livingston, Charles (2002)
Algebraic & Geometric Topology
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Livingston, Charles (2004)
Algebraic & Geometric Topology
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Livingston, Charles (2002)
Geometry & Topology
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Livingston, Charles (2003)
Geometry & 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.
Kirk, P., Livingston, C. (2001)
Geometry & Topology
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Plamenevskaya, Olga (2004)
Algebraic & Geometric Topology
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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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.
Friedl, Stefan (2004)
Algebraic & Geometric Topology
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Willerton, Simon (2002)
Experimental Mathematics
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Denis Petrovich Ilyutko, Vassily Olegovich Manturov, Igor Mikhailovich Nikonov (2014)
Banach Center Publications
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In [12, 15] it was shown that in some knot theories the crucial role is played by parity, i.e. a function on crossings valued in {0,1} and behaving nicely with respect to Reidemeister moves. Any parity allows one to construct functorial mappings from knots to knots, to refine many invariants and to prove minimality theorems for knots. In the present paper, we generalise the notion of parity and construct parities with coefficients from an abelian group rather than ℤ₂ and investigate...
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.