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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Two questions on mapping class groups


Author: Louis Funar
Journal: Proc. Amer. Math. Soc. 139 (2011), 375-382
MSC (2010): Primary 57M07, 20F36, 20F38, 57N05
Published electronically: August 5, 2010
MathSciNet review: 2729098
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Abstract: We show that central extensions of the mapping class group $ M_g$ of the closed orientable surface of genus $ g$ by $ \mathbb{Z}$ are residually finite. Further we give rough estimates of the largest $ N=N_g$ such that homomorphisms from $ M_g$ to $ SU(N)$ have finite image. In particular, homomorphisms of $ M_g$ into $ SL([\sqrt{g+1}],\mathbb{C})$ have finite image. Both results come from properties of quantum representations of mapping class groups.


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Additional Information

Louis Funar
Affiliation: Institut Fourier, BP 74, UMR 5582, University of Grenoble I, 38402 Saint-Martin-d’Hères cedex, France
Email: funar@fourier.ujf-grenoble.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10555-5
PII: S 0002-9939(2010)10555-5
Keywords: Mapping class group, central extension, quantum representation.
Received by editor(s): October 12, 2009
Received by editor(s) in revised form: April 2, 2010
Published electronically: August 5, 2010
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.