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

Let ${\mathcal {K}}_{m}=\{m$-singular knots $\}$

Given $V$ of type $m$, 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.