Kazuhiro Hikami, Anatol N. Kirillov
Abstract
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We reveal an intimate connection between the quantum knot invariant for torus knot T(s,t) and the character of the minimal model M(s,t), where s and t are relatively prime integers. We show that Kashaev's invariant, i.e., the N-colored Jones polynomial at the Nth root of unity, coincides with the Eichler integral of the character.
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We reveal an intimate connection between the quantum knot invariant for torus knot T(s,t) and the character of the minimal model M(s,t), where s and t are relatively prime integers. We show that Kashaev's invariant, i.e., the N-colored Jones polynomial at the Nth root of unity, coincides with the Eichler integral of the character.
Key concepts: Quantum invariant, Jones polynomial, Knot polynomial, Torus, Knot invariant, Knot complement, Mathematics, Combinatorics