Notes for AKT-090917-2/0:20:43

Proof of the theorem from last hour: $j_{(n,\cdot )}$ is a type $n$ invariant. (in fact we may prove the same for both the Conway and HOMFLY-PT polynomial) Substitute $q=e^{x}$ into the Jones skein relation, simplify $J($ double point $)$ and deduce the value of $J$ on a $n+1$ singular knot $\Rightarrow j_{n}$ vanishes on ${\mathcal {K}}_{n+1}$.