Topological Quantum Field Theory and the Nielsen-thurston Classification of M (0, 4)

  title={Topological Quantum Field Theory and the Nielsen-thurston Classification of M (0, 4)},
  author={J\orgen Ellegaard Andersen and Gregor Masbaum and Kenji Ueno},
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, PseudoAnosov mapping classes are represented by matrices of infinite order. 
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