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

Jørgen Ellegaard Andersen

J. Math. Kyoto Univ., Tome 48 (2008) no. 4, p. 323-338 / Harvested from Project Euclid

Résumé

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 $\phi$.

Publié le : 2008-05-15
Classification:

@article{1250271414,
     author = {J\o rgen Ellegaard Andersen},
     title = {The Nielsen-Thurston classification of mapping classes is determined by TQFT},
     journal = {J. Math. Kyoto Univ.},
     volume = {48},
     number = {4},
     year = {2008},
     pages = { 323-338},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250271414}
}

Jørgen Ellegaard Andersen. The Nielsen-Thurston classification of mapping classes is determined by TQFT. J. Math. Kyoto Univ., Tome 48 (2008) no. 4, pp.  323-338. http://gdmltest.u-ga.fr/item/1250271414/