2003/06/19 by S. Baseilhac, R. Benedetti
Mathematics · Physics and Astronomy · #math.GT #hep-th #msc:57M27 #msc:57Q15 #msc:57R20 #msc:20G42
published as Topology 43 (2004) 1373--1423 · 49 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
arxiv created 2003/06/19 · arxiv updated 2009/11/30
We 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 JN(L) of hyperbolic knots L in S3 in the framework of the general QHI theory.