Results 281 to 290 of about 280,204 (322)
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Embedding Knots in Trivial Knots
Bulletin of the London Mathematical Society, 1982The authors show that every knot can be embedded in codimension two in a trivial knot, and they derive corresponding theorems about embedding branched coverings in codimension two. These results (and generalizations) were obtained previously by the reviewer and by W. D. Neumann [Topology 16 (1977), no. 4, 369–393.
Gonzalez-Acuna, F. +1 more
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Virtual Knots with Properties of Kishino's Knot
Tokyo Journal of Mathematics, 2023Kishino's knot is a non-trivial virtual knot that cannot be distinguished from the trivial knot by either the Jones-Kauffman polynomial or the \(n\)-writhe, where the \(n\)-writhe derived from the Gauss diagram of a virtual knot was introduced in [ \textit{S. Satoh} and \textit{K. Taniguchi}, Fundam. Math. 225, 327--341 (2014; Zbl 1302.57033)].
Ohyama, Yoshiyuki, Sakurai, Migiwa
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Journal of Graph Theory, 2000
The equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves and delta-wye moves on knot diagrams are considered. Any graph that is reducible to a graph with no edges by some finite sequence of the unsigned version of the Reidemeister graph moves is called a knot graph.
Steven D. Noble, D. J. A. Welsh
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The equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves and delta-wye moves on knot diagrams are considered. Any graph that is reducible to a graph with no edges by some finite sequence of the unsigned version of the Reidemeister graph moves is called a knot graph.
Steven D. Noble, D. J. A. Welsh
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1963
Almost everyone is familiar with at least the simplest of the common knots, e.g., the overhand knot, Figure 1, and the figure-eight knot, Figure 2. A little experimenting with a piece of rope will convince anyone that these two knots are different: one cannot be transformed into the other without passing a loop over one of the ends, i.e., without ...
Richard H. Crowell, Ralph H. Fox
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Almost everyone is familiar with at least the simplest of the common knots, e.g., the overhand knot, Figure 1, and the figure-eight knot, Figure 2. A little experimenting with a piece of rope will convince anyone that these two knots are different: one cannot be transformed into the other without passing a loop over one of the ends, i.e., without ...
Richard H. Crowell, Ralph H. Fox
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Knot Projections and Knot Coverings
1993In this paper, computer programs are given which draw knot diagrams, knot projections and representations of knot groups into the symmetric group of degree n.
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1993
In this survey on knot spaces the central theorems are presented such as the Gordon-Luecke complement result, Waldhausen’s theorem, hyperbolic and Seifert fibred knots spaces and the Johannson-Jaco-Shalen torus decomposition.
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In this survey on knot spaces the central theorems are presented such as the Gordon-Luecke complement result, Waldhausen’s theorem, hyperbolic and Seifert fibred knots spaces and the Johannson-Jaco-Shalen torus decomposition.
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