Abstract
For each fixed $n \geq 2$ we show how the Nielsen-Thurston classification of mapping classes for a closed surface of genus $g \geq 2$ is determined by the sequence of quantum $SU(n)$-representations $(\rho_k)_{k \in {\mathbb{N}}}$. That this is the case is a consequence of the asymptotic faithfulness property proved in [A3]. We here provide explicit conditions on $(\rho_k (\phi))_{k\in {\mathbb{N}}}$, which determines the Nielsen-Thurston type of any mapping class $\phi$.
Citation
Jørgen Ellegaard Andersen. "The Nielsen-Thurston classification of mapping classes is determined by TQFT." J. Math. Kyoto Univ. 48 (2) 323 - 338, 2008. https://doi.org/10.1215/kjm/1250271414
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