Ordering Knots
Slavik V. Jablan (1999)
Visual Mathematics
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Slavik V. Jablan (1999)
Visual Mathematics
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Dasbach, Oliver T., Hougardy, Stefan (1997)
Experimental Mathematics
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Clark, Bradd Evans (1983)
International Journal of Mathematics and Mathematical Sciences
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Ying-Qing Wu (1993)
Mathematische Annalen
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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...
Livingston, Charles (2001)
Algebraic & Geometric Topology
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Jonathan A. Hillman (1989)
Inventiones mathematicae
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Monica Meissen (1998)
Banach Center Publications
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The minimal number of edges required to form a knot or link of type K is the edge number of K, and is denoted e(K). When knots are drawn with edges, they are appropriately called piecewise-linear or PL knots. This paper presents some edge number results for PL knots. Included are illustrations of and integer coordinates for the vertices of several prime PL knots.
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.
Paul Melvin, Robion Kirby (1978)
Inventiones mathematicae
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Motegi, Kimihiko, Song, Hyun-Jong (2005)
Algebraic & Geometric Topology
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D. Ruberman (1987)
Inventiones mathematicae
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