The Aarhus integral of rational homology 3-spheres II: Invariance and universality

Abstract

We continue the work started in part I (q-alg/9706004) and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Aarhus 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 part I become straight-forward honest diagram-level proofs here. The universality proof is standard and utilizes a simple "locality" property of the Kontsevich integral.

25 pages; minor modifications

Cited by in corpus (10)

• Analyticity of the Free Energy of a Closed 3-Manifold
• Operations and Identities in Tensor Algebra
• The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant
• The Aarhus integral of rational homology 3-spheres III: The Relation with the Le-Murakami-Ohtsuki Invariant
• Alternative versions of the Johnson homomorphisms and the LMO functor
• On the LMO Invariant, the Wheeling Theorem, and the Aarhus Integral
• Finite Type Link Homotopy Invariants
• On the Existence of Finite Type Link Homotopy Invariants
• Finite Type Link Concordance Invariants
• A surgery formula for the 2-loop piece of the LMO invariant of a pair