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From sl(2) Kirby weight systems to the asymptotic 3-manifold invariant

1998/02/15 by Laurent Freidel, Freidel, Laurent
Mathematics · #57M25 #Advanced Operator Algebra Research #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/9802069

27 pages, 19 figures, added references

openalex publication_date 1998/02/15 · arxiv created 1998/03/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a construction of Kirby weight systems associated to sl(2) and valued into the finite field Z/pZ. We show that it is possible to apply this sequence of weight systems on the universal invariant of framed link. We also show that the corresponding sequence admits a Fermat limit, which defines an asymptotic rational homology 3-sphere quantum invariant. Moreover, this asymptotic invariant coincides with the Ohtsuki invariant.

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