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• 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

$\array{ P_{(Y,L,\mu)} &\to& \mathbf{E}\mathbf{B}U(1) \\ \downarrow && \downarrow \\ C(U) &\stackrel{\mu}{\to}& \mathbf{B}^2 U(1) \\ \downarrow^{\mathrlap{\simeq}} \\ X }$
• 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 $n$-gerbes for all $n$ pretty explicitly as $\mathbf{B}^{n+1}U(1)$-bundles (also with connection) is given.

• CommentRowNumber5.
• CommentAuthorUlrik
• CommentTimeAug 28th 2019

Fix link to Chatterjee’s On Gerbs.

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