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).
The hyperbolic volume of knots from quantum dilogarithm
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
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.
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 to the Alexander polynomial.
citing papers explorer
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Generalized Minkowski Theorem for Tetrahedra in ${\rm dS}^3$ and ${\rm AdS}^3$
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).
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Two roles of Alexander in two Kashaev phases
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.
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More on Kashaev limits of the quantum $A$-polynomials
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 to the Alexander polynomial.