Coloring link diagrams and Conway-type polynomial of braids

摘要

In this paper we define and present a simple combinatorial formula for a 3-variable Laurent polynomial invariant I(a, z, t) of conjugacy classes in Artin braid group B_m. We show that the Laurent polynomial I(a,z,t) satisfies the Conway skein relation and the coefficients of the 1-variable polynomial t~(-k)I(a, z, t)|(a=1,t=0) are Vassiliev invariants of braids.