Constructing the Virasoro groups using differential cohomology

Abstract: Abstract: The Virasoro groups are a family of central extensions of ${\rm Diff}^+(S^1)$ by the circle group $\bf T$. In this talk I will discuss recent work, joint with Yu Leon Liu and Christoph Weis, constructing these groups by beginning with a lift of the first Pontrjagin class to "off-diagonal" differential cohomology, then transgressing it to obtain a central extension. Along the way, I will discuss what the Virasoro extensions are and how to recognize them; a brief introduction to differential cohomology; and lifts of characteristic classes to differential cohomology.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

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Topology and Geometry Seminar (Texas, Kansas)