Establishes the Volume Conjecture for the family of double twist knots: the large-N limit of the colored Jones polynomial, evaluated at a root of unity, recovers the hyperbolic volume of the knot complement. The proof introduces the complexified tetrahedron -- a truncated or doubly-truncated tetrahedron with complexified edge lengths and dihedral angles -- and the associated SL(2,C) representation of the knot-group fundamental group, expresses the colored Jones polynomial through the quantum 6j symbol of U_q(sl2), identifies that 6j symbol with the complexified tetrahedron, and extracts the volume by a stationary-phase analysis of the resulting sum.
A quantum-topology research paper (math.GT) by Jun Murakami that proves the Volume Conjecture for the family of double twist knots. The Volume Conjecture predicts that a certain N -> infinity limit o…