On the algebraic unknotting number

The algebraic unknotting number u_a(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) is a lower bound on u_a(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)=u_a(K).

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