A rational surgery formula for the LMO invariant

Dror Bar-Natan and Ruth Lawrence

Abstract: We write a formula for the LMO invariant of a rational homology sphere presented as a rational surgery on a link in S^3. Our main tool is a careful use of the Aarhus 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 formulae 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 fibred spaces. We find that the LMO invariant does not separate lens spaces, is far from separating general Seifert fibred spaces, but does separate Seifert fibred spaces which are integral homology spheres.

Keywords: knot theory, manifold invariants, perturbative expansions, modular forms, TQFT

AMS subject classification: 57M25 11F37 81Q30

Length: 24 pages

Reference: Israel J. Math. 140(2004)29-60

Last updated April 15th, 2018.
ruthel@math.huji.ac.il