@inproceedings{Dimofte2013TheQC,
title={The Quantum Content of the Gluing Equations},
author={Tudor Dan Dimofte and Stavros Garoufalidis},
year={2013}
}

The gluing equations of a cusped hyperbolic 3-manifold M are a system of polynomial equations in the shapes of an ideal triangulation T of M that describe the complete hyperbolic structure of M and its deformations. Given a Neumann-Zagier datum (comprising the shapes together with the gluing equations in a particular canonical form) we define a formal power series with coefficients in the invariant trace field of M that should (a) agree with the asymptotic expansion of the Kashaev invariant to… CONTINUE READING