The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant

Takahito Kuriya; Thang T. Q. Le; Tomotada Ohtsuki

doi:10.1112/jtopol/jts010

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arXiv · 1005.3895

The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant

Takahito Kuriya·Thang T. Q. Le·Tomotada Ohtsuki

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Abstract

We show that the perturbative ${\frak g}$ invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra ${\frak g}$, i.e, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate the quantum invariants of integral homology 3-spheres [13,14,15], this implies that the LMO invariant dominates the quantum invariants of integral homology 3-spheres.

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Takahito Kuriya, Thang T. Q. Le, Tomotada Ohtsuki. 2010-05-21. The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant. https://doi.org/10.1112/jtopol%2Fjts010

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