  For 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.
