An upper bound conjecture for the Yokota invariant

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.

39 pages, 26 figures. Updated with new title and a stronger focus on the upper bound conjecture; accepted for publication at Algebraic and Geometric Topology

References in corpus (2)

• 6j-symbols, hyperbolic structures and the Volume Conjecture
• The volume conjecture for augmented knotted trivalent graphs