$\mathit {SH}(3)$-move and other local moves on knots

Abstract

An $\SH(3)$-move is an unknotting operation on oriented knots introduced by Hoste, Nakanishi and Taniyama. We consider some relationships to other local moves such as a band surgery, $\Gamma_{0}$-move, and $\Delta$-move, and give some criteria for estimating the $\SH(3)$-unknotting number using the Jones, HOMFLYPT, Q polynomials. We also show a table of $\SH(3)$-unknotting numbers for knots with up to 9 crossings.