Constructing the Virasoro Groups Using Differential Cohomology

Abstract

Abstract The Virasoro groups are a family of central extensions of $\textrm{Diff}^+(S^1)$, the group of orientation-preserving diffeomorphisms of $S^1$, by the circle group $\mathbb T$. We give a novel, geometric construction of these central extensions using “off-diagonal” differential lifts of the first Pontryagin class, thus affirmatively answering a question of Freed–Hopkins.