Topological quantum field theory and the Nielsen-Thurston classification of M(0,4)

Abstract

We show that the Nielsen-Thurston classification of mapping classes of the sphere with four marked points is determined by the quantum SU(n) representations, for any fixed n ≥ 2. In the Pseudo-Anosov case we also show that the stretching factor is a limit of eigenvalues of (non-unitary) SU(2)-TQFT representation matrices. It follows that at big enough levels, Pseudo-Anosov mapping classes are represented by matrices of infinite order. © 2006 Cambridge Philosophical Society.