  In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the
notion of intertwining operator algebra, a nonmeromorphic generalization of the
notion of vertex operator algebra involving monodromies. The problem of
constructing intertwining operator algebras from representations of suitable
vertex operator algebras were solved implicitly earlier in [H3]
(q-alg/9505019). In the present paper, we generalize the geometric and operadic
formulation of the notion of vertex operator algebra given in [H1], [H2], [HL1]
(hep-th/9301009), [HL2] and [H6] to the notion of intertwining operator
algebra. We show that the category of intertwining operator algebras of central
charge c is isomorphic to the category of algebras over rational genus-zero
modular functors (certain analytic partial operads) of central charge c
satisfying certain generalized meromorphicity. This result is one main step in
the construction of genus-zero conformal field theories from representations of
vertex operator algebras announced in [H5] (q-alg/9512024). One byproduct of
the proof of the present isomorphism theorem is a geometric construction of
(framed) braid group representations from intertwining operator algebras and
thus from representations of suitable vertex operator algebras.
