Notes for AKT-090910-2/0:27:51

If D' is the knot diagram D with a positive kink added, then

$\left\langle D'\right\rangle =(-A^{-3})\cdot \left\langle D\right\rangle$

$(-A^{3})^{w(D')}=(-A^{3})\cdot (-A^{3})^{w(D)}$

Therefore, $J(D')=J(D)$ and similarly for a negative kink, i.e. the Jones polynomial is invariant under R1.