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 and 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