Dror Bar-Natan, Stavros Garoufalidis, Lev Rozansky and Dylan Thurston
Abstract: Continuing the work started in Aarhus-I and Aarhus-II, we prove the relationship between the Aarhus integral and the invariant Omega (henceforth called LMO) defined by T.Q.T.Le, J.Murakami and T.Ohtsuki. The basic reason for the relationship is that both constructions afford an interpretation as ``integrated holonomies''. In the case of the Aarhus integral, this interpretation was the basis for everything we did in Aarhus-I and Aarhus-II. The main tool we used there was ``formal Gaussian integration''. For the case of the LMO invariant, we develop an interpretation of a key ingredient, the map j_m, as ``formal negative-dimensional integration''. The relation between the two constructions is then an immediate corollary of the relationship between the two integration theories.
Key words: Chord diagrams, chinese characters, Kontsevich integral.
Notes: 9 pages plus references.