Notes for AKT-090917-1/0:23:37

Let ${\mathcal {K}}_{m}=\{m$-singular knots $\}$ We have $V^{(m)}:{\mathcal {K}}_{m}\rightarrow A$, since $V^{(m+1)}=0$, $V^{(m)}$ does not distinguish over crossing and under crossings in ${\mathcal {K}}_{m}$. Let ${\mathcal {D}}_{m}={\mathcal {K}}_{m}/({\mbox{over crossing}}={\mbox{under crossing}})$. Hence the weight system ${\mathcal {D}}_{m}\rightarrow A$ given by $W_{V}=V^{(m)}$ is well-defined.