Some asymptotics of TQFT via skein theory

Details Some asymptotics of TQFT via skein theory Some asymptotics of TQFT via skein theory

2006-04-25

arxiv.org/abs/math/0604533v1

Mathematics

Geometric Topology

12 pages, 2 figures

Scientific paper

For each oriented surface $\Sigma$ of genus $g$ we study a limit of quantum representations of the mapping class group arising in 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 $SL(2,\C)$ 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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