Minimizing the presentation of a knot group.
Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Friedl, Stefan, Teichner, Peter (2005)
Geometry & 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.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Livingston, Charles (2004)
Geometry & Topology
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S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Livingston, Charles (2004)
Algebraic & Geometric Topology
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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.
Eric P. Klassen (1993)
Forum mathematicum
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Livingston, Charles (2003)
Geometry & Topology
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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...
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.