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arXiv · 1701.03999

Virtual unknotting numbers of certain virtual torus knots

Masaharu Ishikawa·Hirokazu Yanagi
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Abstract

The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings on one overstrand into virtual crossings and prove that its virtual unknotting number is equal to the unknotting number of the $(p,q)$-torus knot, i.e. it is (p-1)(q-1)/2.

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Masaharu Ishikawa, Hirokazu Yanagi. 2017-01-15. Virtual unknotting numbers of certain virtual torus knots. https://arxiv.org/abs/1701.03999

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