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

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