Beginning with a diagram of a braid, we produce colored states which satisfy some combinatorial conditions. Each colored state then contributes a certain weight to a sum, which yields Conway's normalization of the Alexander Polynomial. Using some clever identities among quantum integers, we then establish invariance and agreement with the Alexander polynomial directly. These results establish a first step towards potential categorification of the invariant. Time permitting, we will discuss the connnection of this approach to the representation theory of the braid group. |