On the definition and K-theory realization of a modular functor

We present a definition of a (super)-modular functor which includes certain interesting cases that previous definitions do not allow. We also introduce a notion of topological twisting of a modular functor, and construct formally a realization by a 2-dimensional topological field theory valued in twisted K-modules. We discuss, among other things, the N=1-supersymmetric minimal models from the point of view of this formalism.