On the quantum Teichmüller invariants of fibred cusped 3-manifolds

Stéphane Baseilhac (1) , Riccardo Benedetti (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Dipartimento di Matematica [Pisa]

We show that the reduced quantum hyperbolic invariants of pseudo-Anosov diffeomorphisms of punctured surfaces are intertwiners of local representations of the quantum Teichmüller spaces. We characterize them as the only intertwiners that satisfy certain natural cut-and-paste operations of topological quantum field theories and such that their traces define invariants of mapping tori.

Mots clés: Quantum hyperbolic invariants; Local representations; Quantum Teichmüller space; Fibred hyperbolic cusped 3-manifolds

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

Stéphane Baseilhac, Riccardo Benedetti. On the quantum Teichmüller invariants of fibred cusped 3-manifolds. Geometriae Dedicata, 2018, 197, pp.1-32. ⟨10.1007/s10711-017-0315-0⟩. ⟨hal-01812027⟩