Notes for AKT-090917-1/0:11:09

Defining 'derivative' for maps from the space of oriented $n$-singular knots embedded in an oriented copy of $\mathbb {R} ^{3}$ to Abelian group $A$. (Given knot invariant $V$, $V'$ maps $n$-singular knots to sums of $n-1$-singular knots and $V^{(m)}$ maps $m$-singular knots to $A$ )