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Constructing the Virasoro groups using differential cohomology

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Arun Debray, Yu Leon Liu, Christoph Weis

Algebraic Topology · Submitted 20 Dec 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

how it is stated · asserted 1.00 read the record →

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arXiv ID2112.10837 (version 1)
Pith IDPAIJIGOB, Pith's permanent record of this paper and its review
CitationArun Debray, Christoph Weis, Yu Leon Liu. "Constructing the Virasoro groups using differential cohomology." arXiv:2112.10837 (2021). https://pith.science/paper/PAIJIGOB
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,366 input tokens.

What the abstract itself states, as probabilities: claims first 0.15 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.33 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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 $\mathbb T$. 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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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 $\mathbb T$. background 1.00 0.06 0.05 asserted 1.00
s1 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. contribution 0.98 0.96 0.85 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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 $\mathbb T$. 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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How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 12 sentences without a confident label

Compares with 1 paper
Cites as background 14 papers
  • Freed-Hopkins [ref] interpret the Chern-Weil map as providing an isomorphism $(G)≃→Ω^*()$.

    Chern-Weil forms and abstract homotopy theory · Off-diagonal differential characteristic classes · 0.86

  • Differential cohomology comes with a fiber integration map: if $E→B$ is a fiber bundle of manifolds with fiber $S^1$ whose vertical tangent bundle is oriented, fiber integration is a map [equation] Different constructions of this map have been given in [ref] .

    A geometric description of smooth cohomology · Background on differential cohomology · 0.86

  • Differential cohomology comes with a fiber integration map: if $E→B$ is a fiber bundle of manifolds with fiber $S^1$ whose vertical tangent bundle is oriented, fiber integration is a map [equation] Different constructions of this map have been given in [ref] .

    Quadratic functions in geometry, topology,and M-theory · Background on differential cohomology · 0.86

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