Hyperbolic Structure Arising from a Knot Invariant

Kazuhiro Hikami

arxiv: math-ph/0105039 · v1 · submitted 2001-05-28 · 🧮 math-ph · math.MP

Hyperbolic Structure Arising from a Knot Invariant

Kazuhiro Hikami This is my paper

classification 🧮 math-ph math.MP

keywords invariantdilogarithmfunctionknotquantumanaloguearisearising

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We study the knot invariant based on the quantum dilogarithm function. This invariant can be regarded as a non-compact analogue of Kashaev's invariant, or the colored Jones invariant, and is defined by an integral form. The 3-dimensional picture of our invariant originates from the pentagon identity of the quantum dilogarithm function, and we show that the hyperbolicity consistency conditions in gluing polyhedra arise naturally in the classical limit as the saddle point equation of our invariant.

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Shading A-polynomials via huge representations of $U_q(\mathfrak{su}_N)$
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Authors propose shaded A-polynomials A_a(ℓ_b, m_c) for SU(N) via CG chords from huge representations of U_q(su_N) in the classical limit, with examples for knots 3_1, 4_1, 5_1 in su_3.