From state integrals to q-series

Stavros Garoufalidis; Rinat Kashaev

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arXiv · 1304.2705

From state integrals to q-series

Stavros Garoufalidis·Rinat Kashaev

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Abstract

It is well-known to the experts that multi-dimensional state integrals of products of Faddeev's quantum dilogarithm which arise in Quantum Topology can be written as finite sums of products of basic hypergeometric series in q=e^{2\pi i\tau} and \tilde{q}=e^{-2\pi i/\tau}. We illustrate this fact by giving a detailed proof for a family of one-dimensional integrals which includes state-integral invariants of 4_1 and 5_2 knots.

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Stavros Garoufalidis, Rinat Kashaev. 2013-04-09. From state integrals to q-series. https://arxiv.org/abs/1304.2705

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