Quantum Topology


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Volume 4, Issue 3, 2013, pp. 303–351
DOI: 10.4171/QT/41

Published online: 2013-07-02

On the SL(2,ℂ) quantum 6j-symbols and their relation to the hyperbolic volume

Francesco Costantino[1] and Jun Murakami[2]

(1) IRMA, Strasbourg, France
(2) Waseda University, Tokyo, Japan

We generalize the colored Alexander invariant of knots to an invariant of graphs and we construct a face model for this invariant by using the corresponding $6j$-symbols, which come from the non-integral representations of the quantum group ${\mathcal U}_q(\mathrm{sl}_2)$. We call it the $\mathrm{SL}(2, \mathbb C)$-quantum $6j$-symbols, and show their relation to the hyperbolic volume of a truncated tetrahedron.

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Costantino Francesco, Murakami Jun: On the SL(2,ℂ) quantum 6j-symbols and their relation to the hyperbolic volume. Quantum Topol. 4 (2013), 303-351. doi: 10.4171/QT/41