Topological Quantum Field Theory and the Nielsen-Thurston classification of M(0,4)

Jorgen Ellegaard Andersen, Gregor Masbaum, Kenji Ueno

Published 2005-03-21, updated 2006-08-10Version 2

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 integer $n \geq 2$. 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.