## Journal of Mathematics of Kyoto University

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

Jørgen Ellegaard Andersen

#### 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 $\phi$.

#### Article information

Source
J. Math. Kyoto Univ., Volume 48, Number 2 (2008), 323-338.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250271414

Digital Object Identifier
doi:10.1215/kjm/1250271414

Mathematical Reviews number (MathSciNet)
MR2436739

Zentralblatt MATH identifier
1195.57065

#### Citation

Andersen, Jørgen Ellegaard. The Nielsen-Thurston classification of mapping classes is determined by TQFT. J. Math. Kyoto Univ. 48 (2008), no. 2, 323--338. doi:10.1215/kjm/1250271414. https://projecteuclid.org/euclid.kjm/1250271414