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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 30th 2021
   • (edited Jul 30th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added pointer to * [[Ernesto Lupercio]], [[Bernardo Uribe]], Section 7.2 of: *Gerbes over Orbifolds and Twisted K-theory*, Comm. Math. Phys. 245(3): 449-489. ([arXiv:math/0105039](http://arxiv.org/abs/math/0105039), [doi:10.1007/s00220-003-1035-x](https://doi.org/10.1007/s00220-003-1035-x)) Their Prop. 7.2.2 is verbatim the characterization that BCMMS made the definition of "bundle gerbe module" a month and a half later (except that LU focus on open covers instead of more general surjective submersions, but that's not an actual restriction and in any case not the core of the definition). Also added pointer to * [[Marco Mackaay]], _A note on the holonomy of connections in twisted bundles_, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 1, pp. 39-62. ([arXiv:math/0106019](http://arxiv.org/abs/math/0106019), [numdam:CTGDC_2003__44_1_39_0](http://www.numdam.org/item/?id=CTGDC_2003__44_1_39_0)) which essentially recovers Lupercio & Uribe's Def. 7.2.1. From the arXiv timestamps I gather that it must have been an intense couple of weeks for all these auhtors in spring 2001. But Lupercio & Uribe came out first, by a fair margin. And in equivariant generality, right away... <a href="https://ncatlab.org/nlab/revision/diff/bundle+gerbe+module/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/bundle+gerbe+module/6">v6</a>, <a href="https://ncatlab.org/nlab/show/bundle+gerbe+module">current</a>

   I have added pointer to

   • Ernesto Lupercio, Bernardo Uribe, Section 7.2 of: Gerbes over Orbifolds and Twisted K-theory, Comm. Math. Phys. 245(3): 449-489. (arXiv:math/0105039, doi:10.1007/s00220-003-1035-x)

   Their Prop. 7.2.2 is verbatim the characterization that BCMMS made the definition of “bundle gerbe module” a month and a half later (except that LU focus on open covers instead of more general surjective submersions, but that’s not an actual restriction and in any case not the core of the definition).

   Also added pointer to

   • Marco Mackaay, A note on the holonomy of connections in twisted bundles, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 1, pp. 39-62. (arXiv:math/0106019, numdam:CTGDC_2003__44_1_39_0)

   which essentially recovers Lupercio & Uribe’s Def. 7.2.1.

   From the arXiv timestamps I gather that it must have been an intense couple of weeks for all these auhtors in spring 2001. But Lupercio & Uribe came out first, by a fair margin. And in equivariant generality, right away…

   diff, v6, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJul 30th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexOh, wait, now I see. Lupercio & Uribe introduce that Prop. 7.2.2 only in v2, after they must have seen it in BCMMS. Will adjust the wording in the entry once more...

   Oh, wait, now I see. Lupercio & Uribe introduce that Prop. 7.2.2 only in v2, after they must have seen it in BCMMS. Will adjust the wording in the entry once more…

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeFeb 5th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Fei Han]], [[Ruizhi Huang]], [[Varghese Mathai]], *Fractional structures on bundle gerbe modules and fractional classifying spaces* &lbrack;[arXiv:2203.14439](https://arxiv.org/abs/2203.14439)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/bundle+gerbe+module/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/bundle+gerbe+module/7">v7</a>, <a href="https://ncatlab.org/nlab/show/bundle+gerbe+module">current</a>

   added pointer to:

   • Fei Han, Ruizhi Huang, Varghese Mathai, Fractional structures on bundle gerbe modules and fractional classifying spaces [arXiv:2203.14439]

   diff, v7, current