Pith. sign in

REVIEW 4 cited by

The hyperbolic volume of knots from quantum dilogarithm

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv q-alg/9601025 v2 pith:TN7ZK6YQ submitted 1996-01-23 q-alg math.QA

classification q-algmath.QA
keywords hyperboliclinkdilogarithminvariantknotquantumvolumeabsolute
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

  1. Generalized Minkowski Theorem for Tetrahedra in ${\rm dS}^3$ and ${\rm AdS}^3$

    math-ph 2026-05 unverdicted novelty 7.0 of 10

    Four based SO+(1,2) holonomies reconstruct a unique strictly convex tetrahedron in dS^3 or AdS^3, with det G selecting the model and recovering Euclidean cases via SU(2).

  2. Hamiltonian quantization of complex Chern-Simons theory at level-$k$

    hep-th 2025-04 conditional novelty 6.0 of 10

    The physical Hilbert space of complex Chern-Simons theory on an m-holed sphere at even level carries a Fenchel-Nielsen representation in which Wilson loops along pants-decomposition cuts act as multiplication operators.

  3. Two roles of Alexander in two Kashaev phases

    hep-th 2026-05 unverdicted novelty 5.0 of 10

    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.

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

    hep-th 2026-06 unverdicted novelty 3.0 of 10

    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 ...

Pith tools