Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Volume Conjecture and the A-Polynomials -- the
  Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant   We study quantum invariant Z(M) for cusped hyperbolic 3-manifold M. We
construct this invariant based on oriented ideal triangulation of M by
assigning to each tetrahedron the quantum dilogarithm function, which is
introduced by Faddeev in studies of the modular double of the quantum group.
Following Thurston and Neumann-Zagier, we deform a complete hyperbolic
structure of M, and correspondingly we define quantum invariant Z(M_u). This
quantum invariant is shown to give the Neumann--Zagier potential function in
the classical limit, and the A-polynomial can be derived from the potential
function. We explain our construction by taking examples of 3-manifolds such as
complements of hyperbolic knots and punctured torus bundle over the circle.

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The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
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The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol