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

Patrick M. Gilmer
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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.

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Patrick M. Gilmer. 1997-01-30. On the Witten-Reshetikhin-Turaev representations of mapping class groups. https://doi.org/10.1090/s0002-9939-99-04796-6

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