nLab
Vassiliev skein relation

The Vassiliev skein relation is a way to extend knot invariants to singular knots (at least, to singular knots where the only singularities are double points). If $v$ is a knot invariant that takes values in an abelian group, then it is extended to singular knots using the relation

$$v(L_d)=v(L_{+})-v(L_{-})$$v(L_d) = v(L_+) - v(L_-)

where $L_d$ is a singular knot with a double point and $L_{+}$, respectively $L_{-}$, are formed from $L_d$ by replacing the double point by a positively oriented, respectively negatively oriented, crossing.

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category: knot theory