Conway polynomial (knot theory) (source code)

= Conway polynomial
{disambiguate=knot theory}
{c}
{title2=$\nabla_L(z)$}

= Conway polynomial
{c}
{synonym}

The Conway polynomial is normalized by $\nabla_U=1$ for the <unknot>, zero for a split <unlink> with more than one component, and the <skein relation> $\nabla_{L_+}-\nabla_{L_-}=z\nabla_{L_0}$. For a <knot>, the symmetric <Alexander polynomial> with value one at $t=1$ is $\Delta_K(t)=\nabla_K(t^{1/2}-t^{-1/2})$. This fixes the Laurent-unit ambiguity of the <Seifert-matrix presentation of the Alexander module>.