  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.

Geometric Topology;Quantum Algebra