A Move on Diagrams that Generates S-Equivalence of Knots

Abstract

Two knots in three-space are S-equivalent if they are indistinguishable by Seifert matrices. We show that S-equivalence is generated by the doubled-delta move on knot diagrams. It follows as a corollary that a knot has trivial Alexander polynomial if and only if it can be undone by doubled-delta moves.