Abstract.
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 straightforward “philosophical” calculus-level proofs of [Å-I] become straightforward honest diagram-level proofs here. The universality proof is standard and utilizes a simple “locality” property of the Kontsevich integral.
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Bar-Natan, D., Garoufalidis, S., Rozansky, L. et al. The Århus integral of rational homology 3-spheres II: Invariance and universality . Sel. math., New ser. 8, 341–371 (2002). https://doi.org/10.1007/s00029-002-8109-z
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DOI: https://doi.org/10.1007/s00029-002-8109-z