Growth of quantum 6j-symbols and applications to the Volume Conjecture

Giulio Belletti; Renaud Detcherry; Efstratia Kalfagianni; Tian Yang

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arXiv · 1807.03327

Growth of quantum 6j-symbols and applications to the Volume Conjecture

Giulio Belletti·Renaud Detcherry·Efstratia Kalfagianni·Tian Yang

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Abstract

We prove the Turaev-Viro invariants volume conjecture for a "universal" class of cusped hyperbolic 3-manifolds that produces all 3-manifolds with empty or toroidal boundary by Dehn filling. This leads to two-sided bounds on the volume of any hyperbolic 3-manifold with empty or toroidal boundary in terms of the growth rate of the Turaev-Viro invariants of the complement of an appropriate link contained in the manifold. We also provide evidence for a conjecture of Andersen, Masbaum and Ueno (AMU conjecture) about certain quantum representations of surface mapping class groups. A key step in our proofs is finding a sharp upper bound on the growth rate of the quantum $6j-$symbol evaluated at $q=e^{\frac{2\pi i}{r}}.$

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BibTeX RIS

Giulio Belletti, Renaud Detcherry, Efstratia Kalfagianni, Tian Yang. 2018-07-09. Growth of quantum 6j-symbols and applications to the Volume Conjecture. https://arxiv.org/abs/1807.03327

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