Asymptotic expansion of relative quantum invariants

2021/03/28 by Ka Ho Wong, Tian Yang, Wong, Ka Ho +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2103.15056

openalex publication_date 2021/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose Asymptotic Expansion Conjectures of the relative Reshetikhin-Turaev invariants, of the relative Turaev-Viro invariants and of the discrete Fourier transforms of the quantum 6j-symbols, and prove them for families of special cases. The significance of these expansions is that we do not specify the way that the sequence of the colorings converges to the limit. As a consequence, the terms in the expansion will have to depend on the index r, but the dependence is in a way that the terms are purely geometric invariants of the metrics on the underlying manifold and only the metrics vary with r.

Citations

• Asymptotics of quantum 6j symbols
• On the Volume Conjecture for hyperbolic Dehn-filled 3-manifolds along the figure-eight knot
• A relative version of the Turaev-Viro invariants and the volume of hyperbolic polyhedral 3-manifolds

Cited by

• Asymptotics aspects of Teichmüller TQFT for generalized FAMED semi-geometric triangulations

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