On the LMO conjecture

2008/03/12 by Takahito Kuriya, Kuriya, Takahito
Mathematics · #57M27 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M27

paper · pdf · doi:10.48550/arxiv.0803.1732

11 pages, 5 figures

arxiv created 2008/03/12 · openalex publication_date 2008/03/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a proof of the LMO conjecture which say that for any simply connectd simple Lie group G, the LMO invariant of rational homology 3-spheres recovers the perturvative invariant τ^PG. By Habiro-Le theorem, this implies that the LMO invariant is the universal quantum invariant of integral homology 3-spheres.

Citations

• A universal U(1)-RCC invariant of links and rationality conjecture
• Invariants of 3-manifolds via link polynomials and quantum groups

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