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Title: Growth of quantum $6j$-symbols and applications to the Volume Conjecture.
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=e2πir.  more » « less
Award ID(s):
2004155
NSF-PAR ID:
10323851
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of differential geometry
Volume:
120
Issue:
2
ISSN:
0022-040X
Page Range / eLocation ID:
199-229
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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