  In [AU2] we constructed the vacua modular functor based on the sheaf of vacua
theory developed in [TUY] and the abelian analog in [AU1]. We here provide an
explicit isomorphism from the modular functor underlying the skein-theoretic
model for the Witten-Reshetikhin-Turaev TQFT due to Blanchet, Habbeger, Masbaum
and Vogel to the vacua modular functor. This thus provides a geometric
construction of the TQFT constructed first by Witten-Reshetikhin-Turaev from
the quantum group associated to SL(N).
