The Aarhus integral of rational homology 3-spheres III: The Relation with the Le-Murakami-Ohtsuki Invariant

Abstract

Continuing the work started in Part I and II of this series (see q-alg/9706004 and math.QA/9801049), 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 in q-alg/9512002. 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 Parts I and 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.

LaTeX2e, 16 pages, introduction rewritten and computational example added

References in corpus (5)

• Rozansky-Witten invariants via Atiyah classes
• Rozansky-Witten invariants via formal geometry
• The Aarhus integral of rational homology 3-spheres II: Invariance and universality
• Hyper-Kahler Geometry and Invariants of Three-Manifolds
• The Aarhus integral of rational homology 3-spheres I: A highly non trivial flat connection on S^3

Cited by in corpus (3)

• Analyticity of the Free Energy of a Closed 3-Manifold
• The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant
• On the LMO Invariant, the Wheeling Theorem, and the Aarhus Integral