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Mathematics > Geometric Topology

arXiv:1005.3895 (math)
[Submitted on 21 May 2010]

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

Authors: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.
Comments: 30 pages
Subjects: Geometric Topology (math.GT)
MSC classes: 57M27
Cite as: arXiv:1005.3895 [math.GT]
  (or arXiv:1005.3895v1 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.1005.3895
Related DOI: https://doi.org/10.1112/jtopol/jts010

Submission history

From: Tomotada Ohtsuki [view email]
[v1] Fri, 21 May 2010 06:59:47 UTC (39 KB)
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