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

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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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Authors and Affiliations

  1. The Hebrew University, Institute of Mathematics, Giv‚at-Ram, Jerusalem 91904, Israel,¶ e-mail: drorbn@math.huji.ac.il , , , , , , IL

    D. Bar-Natan

  2. Brandeis University, Department of Mathematics, Waltham, MA 02254-9110, USA,¶ current address:¶ School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA,¶ e-mail: stavros@math.gatech.edu, , , , , , US

    S. Garoufalidis

  3. University of Illinois at Chicago, Department of Mathematics, Statistics and Computer Science, Chicago, IL 60607-7045, USA,¶ current address:¶ UNC-CH, Department of Mathematics, CB 3250 Phillips Hall, Chapel Hill, NC 27599-3250, USA,¶ e-mail: rozansky@email.unc.edu, , , , , , US

    L. Rozansky

  4. University of California at Berkeley, Department of Mathematics, Berkeley, CA 94720-3840, USA,¶ current address:¶ Harvard University, Department of Mathematics, Cambridge, MA 02138, USA,¶ e-mail: dpt@math.harvard.edu, , , , , , US

    D. P. Thurston

Authors
  1. D. Bar-Natan
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  2. S. Garoufalidis
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  3. L. Rozansky
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  4. D. P. Thurston
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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

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