Israel Journal of Mathematics

, Volume 140, Issue 1, pp 29–60 | Cite as

A rational surgery formula for the LMO invariant

  • Dror Bar-Natan
  • Ruth Lawrence


We write a formula for the LMO invariant of a rational homology sphere presented as a rational surgery on a link inS 3. Our main tool is a careful use of the Århus integral and the (now proven) “Wheels” and “Wheeling” conjectures of B-N, Garoufalidis, Rozansky and Thurston. As steps, side benefits and asides we give explicit formulas for the values of the Kontsevich integral on the Hopf link and on Hopf chains, and for the LMO invariant of lens spaces and Seifert fibered spaces. We find that the LMO invariant does not separate lens spaces, is far from separating general Seifert fibered spaces, but does separate Seifert fibered spaces which are integral homology spheres.


Lens Space Continue Fraction Expansion Rational Homology Univalent Vertex Link Relation 
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Copyright information

© The Hebrew University Magnes Press 2004

Authors and Affiliations

  • Dror Bar-Natan
    • 1
  • Ruth Lawrence
    • 1
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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