Automorphism Group of k((t)): Applications to the Bosonic String

This paper is concerned with the formulation of a non-pertubative theory of the bosonic string. We introduce a formal group $G$ which we propose as the ``universal moduli space'' for such a formulation. This is motivated because $G$ establishes a natural link between representations of the Virasoro algebra and the moduli space of curves. Among other properties of $G$ it is shown that a ``local'' version of the Mumford formula holds on $G$.