Finite type invariants of ribbon 2-knots. II (Q5929615)

The notion of a ribbon knot can be generalized to higher dimensions, saying that an \(n\)-knot (locally flat \(S^n\) in \(\mathbb{R}^{n+2})\) is ribbon if it bounds a ribbon \((n+1)\)-disc. In previous joint work with \textit{Taizo Kanenobu} [Contemp. Math. 233, 187-196 (1999; Zbl 0929.57014)], the authors defined a notion of finite type invariants for ribbon \(n\)-knots, replacing the crossing change by the unclasping of a ribbon singularity. In the present paper, the structure of the spaces of finite type invariants for ribbon \(n\)-knots is studied, and in particular it is proved that for \(n=2\) they form a symmetric algebra over the coefficients of the Alexander \(2\)-knot polynomial.