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

Jørgen Ellegaard Andersen, G. Masbaum, K. Ueno

Research output: Contribution to journalJournal articleResearchpeer-review

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.
Original languageEnglish
JournalMath. Proc. Camb. Phil. Soc.
Volume141
Pages (from-to)477-488
DOIs
Publication statusPublished - 2006
Externally publishedYes

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