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An upper bound conjecture for the Yokota invariant

Giulio Belletti

Algebraic & Geometric Topology 25 (2025) 645–675
Abstract

We conjecture an upper bound on the growth of the Yokota invariant of polyhedral graphs, extending a previous result on the growth of the 6j-symbol. Using Barrett’s Fourier transform we are able to prove this conjecture in a large family of examples. As a consequence of this result, we prove the Turaev–Viro volume conjecture for a new infinite family of hyperbolic manifolds.

Keywords
quantum invariants, volume, polyhedra
Mathematical Subject Classification
Primary: 57K16, 57K32
References
Publication
Received: 8 January 2021
Revised: 7 August 2023
Accepted: 27 December 2023
Published: 16 May 2025
Authors
Giulio Belletti
Université Paris-Saclay
Orsay
France
IRMP
Université catholique de Louvain
Louvain-la-Neuve
Belgium
https://sites.google.com/view/giulio-bellettis-homepage/

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