Self \(\Delta\)-equivalence of ribbon links
The unknotting operation, or unknotting move, can be considered as an ``alternating'' version of the second Reidemeister move. The \(\Delta\)-move discussed in this paper can be considered as an ``alternating'' version of the third Reidemeister move. Therefore, applications of \(\Delta\)-moves change the knot or link types as does the unknotting move. If all 3 segments involved in a \(\Delta\)-move belong to the same component, a \(\Delta\)-move is called a self-\(\Delta\)-move. Two knots or links are said to be (self)-\(\Delta\)-equivalent if one can be transformed into another by a finite sequence of (self)-\(\Delta\)-moves. In this paper, the author proves that a ribbon link is self-\(\Delta\)-equivalent to a trivial link (Theorem). A proof is diagrammatic. As a natural consequence of the theorem, the author proposes the conjecture: If two links are cobordant in \(R\), then they are self-\(\Delta\)-equivalent.
scientific article; zbMATH DE number 1018464