The Århus integral of rational homology 3-spheres III: Relation with the Le–Murakami–Ohtsuki invariant

• Dror Bar-Natan ^[3] ; Stavros Garoufalidis ^[1] ; Lev Rozansky ^[2] ; Dylan P. Thurston ^[4]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  2. [2] University of Illinois at Chicago

     University of Illinois at Chicago

     City of Chicago, Estados Unidos

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

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 10, Nº. 3, 2004, págs. 305-324
• Idioma: inglés
• DOI: 10.1007/s00029-004-0344-z
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• Resumen

  • Continuing the work started in [Å-I] and [Å-II], we prove the relationship between the Århus integral and the invariant Ω (henceforth called LMO) defined by T.Q.T. Le, J. Murakami and T. Ohtsuki in [LMO]. The basic reason for the relationship is that both constructions afford an interpretation as “integrated holonomies”. In the case of the Århus integral, this interpretation was the basis for everything we did in [Å-I] and [Å-II]. The main tool we used was “formal Gaussian integration”. For the case of the LMO invariant, we develop an interpretation of a key ingredient, the map j m , as “formal negative dimensional integration”. The relation between the two constructions is then an immediate corollary of the relationship between the two integration theories.