On the Witten-Reshetikhin-Turaev representations of mapping class groups

Abstract

We consider a central extension of the mapping class group of a surface with a collection of framed colored points. The Witten-Reshetikhin-Turaev TQFTs associated to SU(2) and SO(3) induce linear representations of this group. We show that the denominators of matrices which describe these representation over a cyclotomic field can be restricted in many cases. In this way, we give a proof of the known result that if the surface is a torus and there are no colored points, the representations have finite image.

AMS-TeX, 7 pages. Notational changes and typos corrected. To appear in Proc. A.M.S

References in corpus (3)

• Invariants for 1-dimensional cohomology classes arising from TQFT
• Turaev-Viro Modules of Satellite knots
• On the TQFT representations of the mapping class groups

Cited by in corpus (7)

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• Congruence and similarity of 3-manifolds
• Problems on invariants of knots and 3-manifolds
• TQFT computations and experiments
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• Irreducibility of some quantum representations of mapping class groups
• On the asymptotics of quantum SU(2) representations of mapping class groups