On the algebraic unknotting number

Abstract

The algebraic unknotting number ua(K) of a knot K was introduced by Hitoshi Murakami. It equals the minimal number of crossing changes needed to turn K into an Alexander polynomial one knot. In a previous paper, the authors used the Blanchfield form of a knot K to define an invariant n(K) and proved that n(K)⩽ua(K) . They also showed that n(K) subsumes all previous classical lower bounds on the (algebraic) unknotting number. In this paper, we prove that n(K)=ua(K) .