Coloring link diagrams and Conway-type polynomial of braids (Q386186)

In this paper the author constructs a 3-variable Laurent polynomial invariant \(I(a,z,t)\) of conjugacy classes in Artins braid group \(B_m\). For any braid \(\alpha\in B_m\) we can form an oriented link diagram \(D\) by the standard closure operation on the braid \(\alpha\). The Laurent polynomial \(I(a,z,t)\) can be defined on the diagram \(D\) and satisfies the Conway Skein relation, that is for any triple of link diagrams \(D_+\), \(D_-\) and \(D_0\) we have NEWLINE\[NEWLINE I(D_+)-I(D_-)=z I(D_0). NEWLINE\]NEWLINE Furthermore the coefficients of the one variable polynomial \(t^{-k} I(a,z,t)|_{a=1,t=o}\) are finite type (or Vassiliev) invariants of braids.