A rational surgery formula for the LMO invariant
By Dror Bar-Natan, R. Lawrence. 2000
54 citations recorded by the source corpus.
We write a formula for the LMO invariant of a rational homology sphere presented as a rational surgery on a link inS3. 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9b538402760f095a0f08072423a04431ac2b0b5c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Jacob Rasmussen
- L. Rozansky
- G. Massuyeau
- Stavros Garoufalidis
- Tomotada Ohtsuki
- Toshie Takata
- S. K. Hansen
- Simon Willerton
In Mathematical Physics
- Jacob Rasmussen
- L. Rozansky
- Stavros Garoufalidis
- Tomotada Ohtsuki
- Toshie Takata
- S. K. Hansen
- Simon Willerton
- G. Massuyeau
Citations in the corpus
- Problems on invariants of knots and 3-manifolds (2004, background): “Takata) For example, the LMO invariants of the lens spaces L(25, 4) and L(25, 9) are equal [37], but their quantum SU(2) invariants for r = 5 are not equal.”