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Asymptotic properties of the quantum representations of the mapping class group


Author: Laurent Charles
Journal: Trans. Amer. Math. Soc. 368 (2016), 7507-7531
MSC (2010): Primary 14D21, 34E10, 53Z05, 53D30, 58Z05
DOI: https://doi.org/10.1090/tran6680
Published electronically: February 10, 2016
MathSciNet review: 3471099
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Abstract: For any surface with genus $ \geqslant 2$, the monodromy of Hitchin's connection is a projective representation of the mapping class group of the surface. We establish two results on the large level limit of these representations. First we prove that these projective representations lift to asymptotic representations. Second we show that under an infinitesimal rigidity assumption the characters of these representations have an asymptotic expansion. This proves the Witten's asymptotic conjecture for mapping tori of surface diffeomorphisms. Our result is not limited to Seifert manifolds and applies to hyperbolic manifolds.


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Additional Information

Laurent Charles
Affiliation: Sorbonne Universités, UPMC Univ Paris 06, Institut de Mathématiques de Jussieu-Paris rive gauche, 75005 Paris, France

DOI: https://doi.org/10.1090/tran6680
Received by editor(s): July 25, 2014
Received by editor(s) in revised form: January 19, 2015
Published electronically: February 10, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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