Quantum hyperbolic invariants of 3-manifolds with PSL(2,C)-characters

Stéphane Baseilhac (1) , Riccardo Benedetti

1 IF - Institut Fourier

A new family of complex valued invariants is defined for closed oriented 3-manifolds, with an embedded link and a flat principal PSL(2,C)-bundle. These invariants are computed as state sums based on quantum dilogarithms, interpreted as matrix-valued functions of suitably decorated hyperbolic ideal tetrahedra.

Mots clés: Quantum dilogarithms; PSL(2; C)-characters; Hyperbolic 3-manifolds; State sum invariants; volume conjecture

Domaines: Topologie géométrique [math.GT]; Algèbres quantiques [math.QA]

Stéphane Baseilhac, Riccardo Benedetti. Quantum hyperbolic invariants of 3-manifolds with PSL(2,C)-characters. Topology, 2004, 43 (6), pp.1373-1423. ⟨hal-00334358⟩