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The Nielsen-Thurston classification of mapping classes is determined by TQFT

Jorgen Ellegaard Andersen
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Abstract

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.

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Jorgen Ellegaard Andersen. 2006-05-01. The Nielsen-Thurston classification of mapping classes is determined by TQFT. https://arxiv.org/abs/math/0605036

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