Constructing the Virasoro Groups Using Differential Cohomology

DOI10.1093/IMRN/RNAD035arXiv2112.10837OpenAlexW4327944153MaRDI QIDQ6182616

Arun Debray, Christoph Weis, Yu Leon Liu

Publication date: 25 January 2024

Published in: Unnamed Author (Search for Journal in Brave)

Abstract: The Virasoro groups are a family of central extensions of $mathrm{Diff}^{+}(S^1)$, the group of orientation-preserving diffeomorphisms of $S^1$, by the circle group $mathbbT$. 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.

Full work available at URL: https://arxiv.org/abs/2112.10837

Mathematics Subject Classification ID

Topological quantum field theories (aspects of differential topology) (57R56) Topological properties of groups of homeomorphisms or diffeomorphisms (57S05) Lie groups (22Exx) Homology and cohomology theories in algebraic topology (55Nxx)

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