The Kashaev and quantum hyperbolic link invariants

Stephane Baseilhac; Riccardo Benedetti

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arXiv · 1101.1851

The Kashaev and quantum hyperbolic link invariants

Stephane Baseilhac·Riccardo Benedetti

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Abstract

We show that the link invariants derived from 3-dimensional quantum hyperbolic geometry can be defined by means of planar state sums based on link diagrams and a new family of enhanced Yang-Baxteroperators (YBO) that we compute explicitly. By a local comparison of the respective YBO's we show that these invariants coincide with the Kashaev specializations of the colored Jones polynomials. As a further application we disprove a conjecture about the semi-classical limits of quantum hyperbolic partition functions, by showing that it conflicts with the existence of hyperbolic links that verify the volume conjecture.

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Stephane Baseilhac, Riccardo Benedetti. 2011-01-10. The Kashaev and quantum hyperbolic link invariants. https://arxiv.org/abs/1101.1851

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