Constructing the Virasoro Groups Using Differential Cohomology

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