2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112614For each fixed n>=2 we show how the Nielsen-Thurston classification of mapping classes for a closed surface of genus g>=2 is determined by the sequence of quantum SU(n) representations, when one considers all levels. That this is the case is a consequence of our asymptotic faithfulness property. We here provide explicit conditions on the image under these representations, which determines the Nielsen-Thurston type of any mapping class.Quantum AlgebraDifferential Geometrytext