Эта публикация цитируется в 4 статьях

Volume conjecture and WKB asymptotics

A. I. Aptekarev, T. V. Dudnikova, D. N. Tulyakov

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047, Moscow, Russia

Аннотация: We consider $q$-difference equations for colored Jones polynomials. These polynomials are invariants for the knots and their asymptotics plays an important role in the famous Volume Conjecture (VC) for the complement of the knot to the $3d$ sphere. We study WKB asymptotic behavior of the $n$th colored Jones polynomial at the point $\exp\{2\pi/N\}$ when $n$ and $N$ tends to infinity and limit of $n/N$ belongs to $[0,1]$ . We state a Theorem on asymptotic expansion of general solutions of the $q$-difference equations. For the partial solutions, corresponding to the colored Jones polynomials, using some heuristic and numeric consideration, we suggest a conjecture on their WKB asymptotics. For the special knots under consideration, this conjecture is in accordance with the VC.

Язык публикации: английский

DOI: 10.1134/S1995080222110051