Year: 2009
Author: Taizo Kanenobu, Yasuyuki Miyazawa
Communications in Mathematical Research , Vol. 25 (2009), Iss. 5 : pp. 433–460
Abstract
An $H(2)$-move is a local move of a knot which is performed by adding a half-twisted band. It is known an $H(2)$-move is an unknotting operation. We define the $H(2)$-unknotting number of a knot $K$ to be the minimum number of $H(2)$-moves needed to transform K into a trivial knot. We give several methods to estimate the $H(2)$-unknotting number of a knot. Then we give tables of $H(2)$-unknotting numbers of knots with up to 9 crossings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-CMR-19362
Communications in Mathematical Research , Vol. 25 (2009), Iss. 5 : pp. 433–460
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: knot $H(2)$-move $H(2)$-unknotting number signature Arf invariant Jones polynomial $Q$ polynomial.