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15 February 2008 Some asymptotics of Topological quantum field theory via skein theory
Julien Marché, Majid Narimannejad
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Duke Math. J. 141(3): 573-587 (15 February 2008). DOI: 10.1215/00127094-2007-006

Abstract

For each oriented surface Σ of genus g, we study a limit of quantum representations of the mapping class group arising in topological quantum field theory (TQFT) derived from the Kauffman bracket. We determine that these representations converge in the Fell topology to the representation of the mapping class group on H(Σ), the space of regular functions on the SL(2,C)-representation variety with its Hermitian structure coming from the symplectic structure of the SU(2)-representation variety. As a corollary, we give a new proof of the asymptotic faithfulness of quantum representations

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Julien Marché. Majid Narimannejad. "Some asymptotics of Topological quantum field theory via skein theory." Duke Math. J. 141 (3) 573 - 587, 15 February 2008. https://doi.org/10.1215/00127094-2007-006

Information

Published: 15 February 2008
First available in Project Euclid: 15 February 2008

zbMATH: 1139.57030
MathSciNet: MR2387432
Digital Object Identifier: 10.1215/00127094-2007-006

Subjects:
Primary: 57M27
Secondary: 37E30, 57M50

Rights: Copyright © 2008 Duke University Press

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Vol.141 • No. 3 • 15 February 2008
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