An upper bound conjecture for the Yokota invariant

Belletti, Giulio

doi:10.2140/agt.2025.25.645

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An upper bound conjecture for the Yokota invariant

Giulio Belletti

Algebraic & Geometric Topology 25 (2025) 645–675

DOI: 10.2140/agt.2025.25.645

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 $6 j$ -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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Volume 25, issue 2 (2025)