INFINITE-GENUS SURFACES AND THE UNIVERSAL GRASSMANNIAN

Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field t heory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus, verifying the inclusion of these surfac es in the Grassmannian. In particular, a subset of the class of O-HD s urfaces can be identified with a subset of the Grassmannian. The conce pt of flux through the ideal boundary is used to study the connection between infinite-genus surfaces and the domain of string perturbation theory. The different roles of effectively closed surfaces and surface s with Dirichlet boundaries in a more complete formulation of string t heory are identified.