Published in Journal of Gökova Geometry Topology, Volume 5 (2011)
Title The Kashaev and quantum hyperbolic link invariants
Author Stéphane Baseilhac and Riccardo Benedetti
We show that the link invariants derived from 3-dimensional quantum hyperbolic geometry can be defined via planar state sums based on link diagrams and a new family of enhanced Yang-Baxter operators (YBO) that we compute explicitly. By a local comparison of the respective YBO's we show that these invariants coincide with Kashaev's specializations of the colored Jones polynomials. As a further application we disprove a conjecture about the semi-classical limits of quantum hyperbolic invariants, by showing that it conflicts with the existence of hyperbolic links that verify the volume conjecture.
Keywords Links, colored Jones polynomials, generalized Alexander invariants, quantum hyperbolic geometry, Yang-Baxter operators, volume conjecture
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Submitted: Oct 6, 2011
Accepted: Nov 25, 2011
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Last updated: December 2011
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