$H(2)$-Unknotting Number of a Knot (Communications in Mathematical Research, 2021)
An $H(2)$-move is a local move of a knot which is performed by adding ahalf-twisted band. It is known an $H(2)$-move is an unknotting operation. We definethe $H(2)$-unknotting number of a knot $K$ to be the minimum number of $H(2)$-movesneeded 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 numbersof knots with up to 9 crossings.
Keywords: knot; $H(2)$-move; $H(2)$-unknotting number; signature; Arf invariant; Jones polynomial; $Q$ polynomial.