1998/02/06 by Thang T. Q. Lê, Thang T. Q. Le, Le, Thang T. Q.
Mathematics · #57M25 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M25
paper · pdf · doi:10.48550/arxiv.math/9802032
36 Pages. Minor mistakes corrected. Main results slightly improved. Some parts substantially revised
openalex publication_date 1998/02/06 · arxiv created 1998/05/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct power series invariants of rational homology 3-spheres from quantum PSU(n)-invariants. The power series can be regarded as perturbative invariants corresponding to the contribution of the trivial connection in the hypothetical Witten's integral. This generalizes a result of Ohtsuki (the n=2 case) which led him to the definition of finite type invariants of 3-manifolds. The proof utilizes some symmetry properties of quantum invariants (of links) derived from the theory of affine Lie algebras and the theory of the Kontsevich integral.