full
search.png

Search

close.png

Cancel

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

Taizo Kanenobu & Yasuyuki Miyazawa

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

Published online: 2021-07

Preview Purchase PDF 2507 29914

Cited by

google scholar semantic scholar
Export citation
  • 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.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CMR-25-433, author = {Kanenobu , Taizo and Miyazawa , Yasuyuki}, 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.

Kanenobu , Taizo and Miyazawa , Yasuyuki. (2021). $H(2)$-Unknotting Number of a Knot. Communications in Mathematical Research . 25 (5). 433-460. doi:
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard