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

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

[math]\displaystyle{ \left\langle D' \right\rangle =(-A^{-3})\cdot \left\langle D \right\rangle }[/math]

[math]\displaystyle{ (-A^3)^{w(D')}=(-A^3) \cdot (-A^3)^{w(D)} }[/math]

Therefore, [math]\displaystyle{ J(D')=J(D) }[/math] and similarly for a negative kink, i.e. the Jones polynomial is invariant under R1.