Notes for AKT-090917-1/0:20:08

Definition: A knot invariant $V$ is of Vassiliev type $m$ if $V^{(m+1)}=0$ (on the whole space of $(m+1)$-singular knots).

Notation: We drop the superscript in $V^{(m)}$ since for each $m$, $V^{(m)}$ is only defined for $m$-singular knots.

We can also express the 'type $m$' condition as:

Failed to parse (unknown function "\doublepoint"): {\displaystyle V(\doublepoint ... \doublepoint)=0}

whenever we have more than $m$ double points.