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

• D. Bar-Natan ^[3] ; S. Garoufalidis ^[1] ; L. Rozansky ^[2] ; D.P. Thurston ^[4]
  1. [1] Brandeis University

     Brandeis University

     City of Waltham, Estados Unidos

     
  2. [2] University of Illinois at Chicago

     University of Illinois at Chicago

     City of Chicago, Estados Unidos

     
  3. [3] The Hebrew University, Institute of Mathematics, Israel
  4. [4] University of California at Berkeley, Department of Mathematics, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 8, Nº. 3, 2002, págs. 341-371
• Idioma: inglés
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• Resumen

  • 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.