  We study the Madsen-Tillmann spectrum $\C P^\infty_{-1}$ as a quotient of the
Mahowald pro-object $\C P^{\infty}_{-\infty}$, which is closely related to the
Tate cohomology of circle actions. That theory has an associated symplectic
structure, whose symmetries define the Virasoro operations on the cohomology of
moduli space constructed by Kontsevich and Witten.
