Topological quantum field theory and the Nielsen-Thurston classification of M(0,4)

Jørgen Ellegaard Andersen, G. Masbaum, K. Ueno

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

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.
OriginalsprogEngelsk
TidsskriftMath. Proc. Camb. Phil. Soc.
Vol/bind141
Sider (fra-til)477-488
DOI
StatusUdgivet - 2006
Udgivet eksterntJa

Fingeraftryk

Topological Quantum Field Theory
Pseudo-Anosov
Matrix Representation
Eigenvalue
Class

Citer dette

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Topological quantum field theory and the Nielsen-Thurston classification of M(0,4). / Andersen, Jørgen Ellegaard; Masbaum, G.; Ueno, K.

I: Math. Proc. Camb. Phil. Soc., Bind 141, 2006, s. 477-488.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

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.

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DO - 10.1017/S0305004106009698

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JO - Math. Proc. Camb. Phil. Soc.

JF - Math. Proc. Camb. Phil. Soc.

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