On knots in algebraic number theory.
Wolfram Jehne (1979)
Journal für die reine und angewandte Mathematik
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Wolfram Jehne (1979)
Journal für die reine und angewandte Mathematik
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Xingru Zhang (1991)
Fundamenta Mathematicae
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Eva Bayer-Fluckiger (1983)
Commentarii mathematici Helvetici
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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...
S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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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.
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Ying-Qing Wu (1993)
Mathematische Annalen
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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...
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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A. Hatcher, W. Thurston (1985)
Inventiones mathematicae
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P. V. Koseleff, D. Pecker (2014)
Banach Center Publications
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We show that every knot can be realized as a billiard trajectory in a convex prism. This proves a conjecture of Jones and Przytycki.
Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
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Corinne Cerf (2002)
Visual Mathematics
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