  Generalized connections and their calculus have been developed in the context
of quantum gravity. Here we apply them to abelian Chern-Simons theory. We
derive the expectation values of holonomies in U(1) Chern-Simons theory using
Stokes' theorem, flux operators and generalized connections. A framing of the
holonomy loops arises in our construction, and we show how, by choosing natural
framings, the resulting expectation values nevertheless define a functional
over gauge invariant cylindrical functions.
  The abelian theory considered in the present article is test case for our
method. It can also be applied to the non-abelian theory. Results for that case
will be reported elsewhere.
