Optimistic limit of the colored Jones polynomial and the existence of a solution

Cho, Jinseok

doi:10.1090/proc/12845

Optimistic limit of the colored Jones polynomial and the existence of a solution
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by Jinseok Cho PDF

Proc. Amer. Math. Soc. 144 (2016), 1803-1814 Request permission

Abstract:

For the potential function of a link diagram induced by the optimistic limit of the colored Jones polynomial, we show the existence of a solution of the hyperbolicity equations by directly constructing it. This construction is based on the shadow-coloring of the conjugation quandle induced by a boundary-parabolic representation $\rho :\pi _1(L)\rightarrow \textrm {PSL}(2,\mathbb {C})$. This gives us a very simple and combinatorial method to calculate the complex volume of $\rho$.

References

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