TY - JOUR
T1 - Topological quantum field theory and the Nielsen-Thurston classification of M(0,4)
AU - Andersen, Jørgen Ellegaard
AU - Masbaum, G.
AU - Ueno, K.
PY - 2006
Y1 - 2006
N2 - 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 $n\geq 2$. 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.
AB - 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 $n\geq 2$. 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.
U2 - 10.1017/S0305004106009698
DO - 10.1017/S0305004106009698
M3 - Journal article
VL - 141
SP - 477
EP - 488
JO - Math. Proc. Camb. Phil. Soc.
JF - Math. Proc. Camb. Phil. Soc.
ER -