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nLab > Latest Changes: bundle gerbe

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 9th 2010
    • (edited Sep 9th 2010)

    i polished the definition in bundle gerbe and then reorganized the former material on “Interpretations” in a new section

    that first shows how to get a shifted central extension of groupoids form the bundle gerbe, and then demonstrates that this is the total space of a principal 2-bundle

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 9th 2010
    • (edited Sep 9th 2010)

    added to bundle gerbe more details on the proof of the fact that the bundle gerbe is the pullback

    P (Y,L,μ) → EBU(1) ↓ ↓ C(U) →μ B 2U(1) ↓ ≃ X \array{ P_{(Y,L,\mu)} &\to& \mathbf{E}\mathbf{B}U(1) \\ \downarrow && \downarrow \\ C(U) &\stackrel{\mu}{\to}& \mathbf{B}^2 U(1) \\ \downarrow^{\mathrlap{\simeq}} \\ X }
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 12th 2010

    added two examples to bundle gerbe:

    • group extensions (=equivariant bundle gerbes over the point)

    • the construction of the “tautological bundle gerbe” from an integral closed 3-form on a simply connected manifold

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 22nd 2011

    I have added a pointer to the 1997 article by Gajer to bundle gerbe, bundle 2-gerbe and circle n-bundle with connection, where bundle nn-gerbes for all nn pretty explicitly as B n+1U(1)\mathbf{B}^{n+1}U(1)-bundles (also with connection) is given.

    • CommentRowNumber5.
    • CommentAuthorUlrik
    • CommentTimeAug 28th 2019

    Fix link to Chatterjee’s On Gerbs.

    diff, v25, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeSep 13th 2020

    added pointer to:

    diff, v27, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 20th 2020

    added pointer to

    diff, v28, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeDec 20th 2021
    • (edited Dec 20th 2021)

    started (here) compiling a list with references on equivariant bundle gerbes.

    (Will probably create a new entry equivariant infinity-bundle and copy this over to there, too.)

    diff, v29, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeDec 21st 2021

    an earlier discussion of general equivariant bundle gerbes (verbalized as Deligne cocycles):

    diff, v30, current

  10. Added reference.

    S. Bunk

    diff, v32, current

  11. Fixed typo.

    S. Bunk

    diff, v32, current

1 to 11 of 11

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