Constructing the Virasoro Groups Using Differential Cohomology

Arun Debray; Yu Leon Liu; Christoph Weis

doi:10.1093/imrn/rnad035

Constructing the Virasoro Groups Using Differential Cohomology

Arun Debray, Yu Leon Liu, Christoph Weis

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The Virasoro groups are a family of central extensions of Diff⁺(S¹), the group of orientation-preserving diffeomorphisms of S¹, 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.

Original language	English
Pages (from-to)	18537-18574
Number of pages	38
Journal	International Mathematics Research Notices
Volume	2023
Issue number	21
DOIs	https://doi.org/10.1093/imrn/rnad035
State	Published - Nov 1 2023

Bibliographical note

Publisher Copyright:
© 2023 Oxford University Press. All rights reserved.

Funding

Most of all we would like to thank Dan Freed and Mike Hopkins for sharing their question, which inspired this paper, and for many helpful mathematical discussions. This paper also benefited from conversations with Araminta Amabel, Sanath Devalapurkar, Peter Haine, André Henriques, Ralph Kauffman, Cameron Krulewski, Kiran Luecke, Natalia Pacheco-Tallaj, Wyatt Reeves, Charlie Reid, and Jim Stasheff; thank you to all.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1093/imrn/rnad035

Cite this

@article{b63f4c386be5451aac43d3dc6b706dfd,

title = "Constructing the Virasoro Groups Using Differential Cohomology",

abstract = "The Virasoro groups are a family of central extensions of Diff+(S1), the group of orientation-preserving diffeomorphisms of S1, 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.",

author = "Arun Debray and Liu, \{Yu Leon\} and Christoph Weis",

year = "2023",

month = nov,

day = "1",

doi = "10.1093/imrn/rnad035",

language = "English",

volume = "2023",

pages = "18537--18574",

number = "21",

}

TY - JOUR

T1 - Constructing the Virasoro Groups Using Differential Cohomology

AU - Debray, Arun

AU - Liu, Yu Leon

AU - Weis, Christoph

PY - 2023/11/1

Y1 - 2023/11/1

N2 - The Virasoro groups are a family of central extensions of Diff+(S1), the group of orientation-preserving diffeomorphisms of S1, 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.

AB - The Virasoro groups are a family of central extensions of Diff+(S1), the group of orientation-preserving diffeomorphisms of S1, 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.

UR - http://www.scopus.com/inward/record.url?scp=85178312873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85178312873&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnad035

DO - 10.1093/imrn/rnad035

M3 - Article

AN - SCOPUS:85178312873

SN - 1073-7928

VL - 2023

SP - 18537

EP - 18574

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 21

ER -

Constructing the Virasoro Groups Using Differential Cohomology

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this