2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169430An earlier article with Francis Bonahon introduced new invariants for pseudo-Anosov diffeomorphisms of surface, based on the representation theory of the quantum Teichmuller space. We explicity compute these quantum hyperbolic invariants in the case of the 1-puncture torus and the 4-puncture sphere.A mistake was correctedGeometric TopologyQuantum Algebra57R56; 57M50; 20G42text