Ribbon-moves for 2-knots with 1-handles Attached and Khovanov-jacobsson Numbers

We prove that a crossing change along a double point circle on a 2-knot is realized by ribbon-moves for a knotted torus obtained from the 2-knot by attaching a 1-handle. It follows that any 2-knots for which the crossing change is an unknotting operation, such as ribbon 2-knots and twistspun knots, have trivial Khovanov-Jacobsson number. A surface-knot or -link is a closed surface embedded in 4-space R locally flatly. Throughout this note, we always assume that all surface-knots are oriented. A ribbon-move (cf. [10]) is a local operation for (a diagram of) a surface-knot as shown in Figure 1. We say that surface-knots F and F ′ are ribbon-move equivalent, denoted by F ∼ F , if F ′ is obtained from F by a finite sequence of ribbon-moves.