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 - <p style="text-align: justify;">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.</p>