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

Abstract

We show that the perturbative $\mathfrak{g}$ invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra $\mathfrak{g}$, 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.

30 pages

References in corpus (3)

• On the quantum sl_2 invariants of knots and integral homology spheres
• A Unified Quantum SO(3) Invariant for Rational Homology 3-Spheres
• On the LMO conjecture

Cited by in corpus (2)

• Unified quantum invariants for integral homology spheres associated with simple Lie algebras
• An extension of the LMO functor