The Jones polynomial of ribbon links

The idea of the talk is to study the behaviour of the Jones polynomial for ribbon knots. We will show that for an n-component ribbon link, the nullity (multiplicity of the zero at q = i) of the Jones polynomial is exactly n − 1 i.e Null(V(q))=n+1. First, the upper bound part i.e Null(V(q))<=n+1 (for any link), will follow from an algebraic study of the Jones polynomial. Second, the strategy of proof for the lower bound i.e Null(V(q))>=n+1  (for ribbon links) come from applying Kauffman skein relations to ribbon band moves.The consequences of this result will be outlined in a second part of the talk, with notably the notion of surface invariants of finite type with respect to band crossing changes.