Abstract

We consider \(q\)-difference equations for colored Jones polynomials. These sequences of polynomials are invariants for the knots and their asymptotics plays an important role in the famous volume conjecture for the complement of the knot to the \(3\)d sphere. We give an introduction to the theory of hyperbolic volume of the knots complements and study the asymptotics of the solutions of \(q\)-recurrence relations of high order.

中文翻译：

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有色琼斯多项式的递归关系和渐近线

摘要

我们考虑\(q\) -彩色琼斯多项式的差分方程。这些多项式序列是结的不变量，它们的渐近性在著名的体积猜想中起着重要作用，即结对\(3\) d 球体的补集。介绍了结补的双曲体积理论，研究了\(q\)-高阶递归关系解的渐近性。