Unknotting Number, Genus, and Companion Tori.
Martin Scharlemann, Abigail Thompson (1988)
Mathematische Annalen
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Martin Scharlemann, Abigail Thompson (1988)
Mathematische Annalen
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Clark, Bradd Evans (1983)
International Journal of Mathematics and Mathematical Sciences
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Lisca, Paolo, Stipsicz, András I. (2004)
Geometry & Topology
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Florens, Vincent, Gilmer, Patrick M. (2003)
Algebraic & Geometric Topology
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Cavicchioli, Alberto, Spaggiari, Fulvia (2006)
International Journal of Mathematics and Mathematical Sciences
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Erbland, John, Guterriez, Mauricio (1991)
International Journal of Mathematics and Mathematical Sciences
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A. Stoimenow (2008)
Fundamenta Mathematicae
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We give a description of all knot diagrams of canonical genus 2 and 3, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3- and 4-move conjectures, and the calculation of the maximal hyperbolic volume for canonical (weak) genus 2 knots. We also study the values of the link polynomials at roots of unity, extending denseness results of Jones. Using...
Livingston, Charles (2004)
Algebraic & Geometric Topology
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K. Motegi (1996)
Revista Matemática de la Universidad Complutense de Madrid
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Let K (resp. L) be a Montesinos knot (resp. link) with at least four branches. Then we show the unknotting number (resp. unlinking number) of K (resp. L) is greater than 1.
Livingston, Charles (2004)
Geometry & Topology
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Ozsváth, Peter, Szabó, Zoltán (2003)
Geometry & Topology
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Alberto Cavicchioli (1985)
Collectanea Mathematica
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Dean, John C. (2003)
Algebraic & Geometric Topology
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