Constructing the Virasoro Groups Using Differential Cohomology

The Virasoro groups are a family of central extensions of Diff(S), the group of orientation-preserving diffeomorphisms of S, by the circle group 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.

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