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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 twist-spun knots, have trivial Khovanov-Jacobsson number.
In this paper, we prove that given two cubical links of dimension two in ${mathbb R}^4$, they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the Reidemeister and Ro
We prove that the crossing changes, Delta moves, and sharp moves are unknotting operations on welded knots.
The fusion number of a ribbon knot is the minimal number of 1-handles needed to construct a ribbon disk. The strong homotopy fusion number of a ribbon knot is the minimal number of 2-handles in a handle decomposition of a ribbon disk complement. We d
The writhe polynomial is a fundamental invariant of an oriented virtual knot. We introduce a kind of local moves for oriented virtual knots called shell moves. The first aim of this paper is to prove that two oriented virtual knots have the same writ
Conway-normalized Alexander polynomial of ribbon knots depend only on their ribbon diagrams. Here ribbon diagram means a ribbon spanning the ribbon knot marked with the information of singularities. We further give an algorithm to calculate Alexander