## Duke Mathematical Journal

### Some asymptotics of Topological quantum field theory via skein theory

#### Abstract

For each oriented surface $\Sigma$ 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 $\boH(\Sigma)$, the space of regular functions on the ${\rm SL}(2,\C)$-representation variety with its Hermitian structure coming from the symplectic structure of the ${\rm SU}(2)$-representation variety. As a corollary, we give a new proof of the asymptotic faithfulness of quantum representations

#### Article information

Source
Duke Math. J., Volume 141, Number 3 (2008), 573-587.

Dates
First available in Project Euclid: 15 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1203087638

Digital Object Identifier
doi:10.1215/00127094-2007-006

Mathematical Reviews number (MathSciNet)
MR2387432

Zentralblatt MATH identifier
1139.57030

#### Citation

Marché, Julien; Narimannejad, Majid. Some asymptotics of Topological quantum field theory via skein theory. Duke Math. J. 141 (2008), no. 3, 573--587. doi:10.1215/00127094-2007-006. https://projecteuclid.org/euclid.dmj/1203087638

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