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

Dror Bar-Natan·Stavros Garoufalidis·Lev Rozansky·Dylan Thurston
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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.

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Dror Bar-Natan, Stavros Garoufalidis, Lev Rozansky, Dylan Thurston. 1999-02-15. The Aarhus integral of rational homology 3-spheres II: Invariance and universality. https://arxiv.org/abs/math/9801049

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