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


Author: Patrick M. Gilmer
Journal: Proc. Amer. Math. Soc. 127 (1999), 2483-2488
MSC (1991): Primary 57M99
DOI: https://doi.org/10.1090/S0002-9939-99-04796-6
Published electronically: April 15, 1999
MathSciNet review: 1487369
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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 representations 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 with no colored points, the representations have finite image.


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Additional Information

Patrick M. Gilmer
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: gilmer@math.lsu.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04796-6
Keywords: Mapping class group, TQFT
Received by editor(s): June 23, 1997
Received by editor(s) in revised form: November 5, 1997
Published electronically: April 15, 1999
Additional Notes: This research was partially supported by a grant from the Louisiana Education Quality Support Fund.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1999 American Mathematical Society

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