Constructing TQFTs from Modular Functors

We prove in this paper that any 2 dimensional modular functor satisfying that S-1,(1) not equal 0 induces a family of 2 + I dimensionally topological quantum field theories. We do this for two kinds of modular functors namely a modular functor on the category of extended surfaces and a modular functor on the category of extended surfaces with marked points and directions. We follow the ideas of M. Kontsevich, [21], and K. Walker, [32] but we give proofs and provide details left out in [21] and [32]. Careful study also shows that more choices are needed to define the TQFT than it is revealed in [21] and [32]. Oil the other hand, relations found in [32] turns out not to be needed here.