  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 $G$.
