The Jones polynomial of ribbon links

  title={The Jones polynomial of ribbon links},
  author={Michael Eisermann},
For everyn–component ribbon linkL we prove that the Jones polynomial V(L) is divisible by the polynomial V(©n) of the trivial link. This integrality property allows us to define a generalized determinant det V(L) := [V(L)/V(©)](t 7→−1) , for which we derive congruences reminiscent of the Arf invar iant: every ribbon link L = K1∪· · ·∪Kn satisfies det V(L) ≡ det(K1) · · · det(Kn) modulo 32, whence in particular det V(L) ≡ 1 modulo 8.