Stavros Garoufalidis and Yueheng Lan
Abstract: The Hyperbolic Volume Conjecture loosely states that the limit of the $n$-th colored Jones polynomial of a hyperbolic knot, evaluated at the primitive complex $n$-th root of unity is a sequence of complex numbers that grows exponentially. Moreover, the exponential grwoth rate is proportional to the hyperbolic volume of the knot. We provide numerical evidence for the Hyperbolic Volume Conjecture for the simplest hyperbolic non-2-bridge knot.
Key words: $q$-difference equations, asymptotics, Jones polynomial, Hyperbolic Volume Conjecture, character varieties, recursion relations, Kauffman bracket, skein module, fusion, snappea, m082.
Notes: 15 pages, 6 figures.