The Århus Integral of Rational Homology 3-spheres Ii: Invariance and Universality

We continue the work started in [Å-I], and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Århus integral of rational homology 3-spheres. Our main tool in proving invariance is a translation scheme that translates statements in multi-variable calculus (Gaussian integration, integration by parts, etc.) to statements about diagrams. Using this scheme the straight-forward “philosophical” calculus-level proofs of [Å-I] become straight-forward honest diagram-level proofs here. The universality proof is standard and utilizes a simple “locality” property of the Kontsevich integral.