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

Jorgen Ellegaard Andersen·Gregor Masbaum·Kenji Ueno
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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 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.

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Jorgen Ellegaard Andersen, Gregor Masbaum, Kenji Ueno. 2006-08-10. Topological Quantum Field Theory and the Nielsen-Thurston classification of M(0,4). https://arxiv.org/abs/math/0503414

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