Volume 25, Issue 5
$H(2)$-Unknotting Number of a Knot

Commun. Math. Res., 25 (2009), pp. 433-460.

Published online: 2021-07

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• 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.

• Keywords

knot, $H(2)$-move, $H(2)$-unknotting number, signature, Arf invariant, Jones polynomial, $Q$ polynomial.

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@Article{CMR-25-433, author = {Taizo and Kanenobu and and 17487 and and Taizo Kanenobu and Yasuyuki and Miyazawa and and 17488 and and Yasuyuki Miyazawa}, title = {$H(2)$-Unknotting Number of a Knot}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {5}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19362.html} }
TY - JOUR T1 - $H(2)$-Unknotting Number of a Knot AU - Kanenobu , Taizo AU - Miyazawa , Yasuyuki JO - Communications in Mathematical Research VL - 5 SP - 433 EP - 460 PY - 2021 DA - 2021/07 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19362.html KW - knot, $H(2)$-move, $H(2)$-unknotting number, signature, Arf invariant, Jones polynomial, $Q$ polynomial. AB -

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.

Taizo Kanenobu & Yasuyuki Miyazawa. (2021). $H(2)$-Unknotting Number of a Knot. Communications in Mathematical Research . 25 (5). 433-460. doi:
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