Quantum Hyperbolic Invariants Of 3-Manifolds With PSL(2,C)-Characters

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dc.creatorBaseilhac, S.
dc.creatorBenedetti, R.
dc.date2003-06-19
dc.date.accessioned2026-07-07T04:59:03Z
dc.date.available2026-07-07T04:59:03Z
dc.descriptionWe construct {\it quantum hyperbolic invariants} (QHI) for triples $(W,L,ρ)$, where $W$ is a compact closed oriented 3-manifold, $ρ$ is a flat principal bundle over $W$ with structural group $PSL(2,\mc)$, and $L$ is a non-empty link in $W$. These invariants are based on the Faddeev-Kashaev's {\it quantum dilogarithms}, interpreted as matrix valued functions of suitably decorated hyperbolic ideal tetrahedra. They are explicitely computed as state sums over the decorated hyperbolic ideal tetrahedra of the {\it idealization} of any fixed {\it $\Dd$-triangulation}; the $\Dd$-triangulations are simplicial 1-cocycle descriptions of $(W,ρ)$ in which the link is realized as a Hamiltonian subcomplex. We also discuss how to set the Volume Conjecture for the coloured Jones invariants $J_N(L)$ of hyperbolic knots $L$ in $S^3$ in the framework of the general QHI theory.
dc.description49 pages, 17 figures. Together with our paper `Classical And Quantum Dilogarithmic Invariants Of Flat PSL(2,C)-Bundles Over 3-Manifolds' avalaible on the same ArXiv, this develops with full details the results announced in math.GT/0211061
dc.identifierhttps://arxiv.org/abs/math/0306280
dc.identifierhttp://arxiv.org/abs/math/0306280
dc.identifierTopology 43 (2004) 1373--1423
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67827
dc.subjectGeometric Topology
dc.subjectHigh Energy Physics - Theory
dc.subject57M27,57Q15;57R20,20G42
dc.titleQuantum Hyperbolic Invariants Of 3-Manifolds With PSL(2,C)-Characters
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