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Topological Quantum Field Theory and the Nielsen–Thurston classification of $M(0,4)$

Published online by Cambridge University Press:  01 December 2006

JØRGEN ELLEGAARD ANDERSEN ,
GREGOR MASBAUM  and
KENJI UENO
JØRGEN ELLEGAARD ANDERSEN
Affiliation:
Department of Mathematics, University of Aarhus, DK-8000 Aarhus C, Denmark. e-mail: andersen@imf.au.dk
GREGOR MASBAUM
Affiliation:
Institut de Mathématiques de Jussieu (UMR 7586 du CNRS) Université Paris 7 (Denis Diderot), Case 7012, 75251 Paris Cedex 05, France. e-mail: masbaum@math.jussieu.fr
KENJI UENO
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-01, Japan. e-mail: ueno@math.kyoto-u.ac.jp
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 3 , November 2006 , pp. 477 - 488
Copyright
© 2006 Cambridge Philosophical Society

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