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-Baxter operators (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.
The Kashaev and quantum hyperbolic link invariants
BENEDETTI, RICCARDO
2011-01-01
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-Baxter operators (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.File in questo prodotto:
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