pith. sign in

arxiv: q-alg/9601025 · v2 · submitted 1996-01-23 · q-alg · math.QA

The hyperbolic volume of knots from quantum dilogarithm

classification q-alg math.QA
keywords hyperboliclinkdilogarithminvariantknotquantumvolumeabsolute
0
0 comments X
read the original abstract

The invariant of a link in three-sphere, associated with the cyclic quantum dilogarithm, depends on a natural number $N$. By the analysis of particular examples it is argued that for a hyperbolic knot (link) the absolute value of this invariant grows exponentially at large $N$, the hyperbolic volume of the knot (link) complement being the growth rate.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Two roles of Alexander in two Kashaev phases

    hep-th 2026-05 unverdicted novelty 5.0

    Alexander polynomials appear in two opposite roles in two Kashaev phases of Chern-Simons theory due to co-existing branches in the quasiclassical limit with non-trivial versus vanishing classical actions.

  2. More on Kashaev limits of the quantum $A$-polynomials

    hep-th 2026-06 unverdicted novelty 3.0

    In the Kashaev limit the non-homogeneous quantum A-polynomial splits into phases tied to zero action and deformed hyperbolic volume, with a byproduct expectation that the classical A-polynomial at L=1 is proportional ...