Shranjeno v:
| Glavni avtor: | |
|---|---|
| Format: | Preprint |
| Izdano: |
2026
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| Teme: | |
| Online dostop: | https://arxiv.org/abs/2602.01049 |
| Oznake: |
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Kazalo:
- We study the asymptotic behavior, as $N$ tends to infinity, of the $N$-dimensional colored Jones polynomial of the figure-eight knot, evaluated at $\exp(ξ/N)$ for a complex parameter $ξ$ with $0<\mathrm{Im}ξ<π/2$. We prove that if $\mathrm{Re}ξ$ is large the colored Jones polynomial grows exponentially with growth rate expressed by the Chern--Simons invariant, and that if $\mathrm{Re}ξ$ is small it converges to the reciprocal of the Alexander polynomial evaluated at $\expξ$.