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Atrium > Mathematics, Physics & Philosophy: G-Gerbes (or really G2-torsors?)

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    • CommentRowNumber1.
    • CommentAuthorrdkw10
    • CommentTimeFeb 24th 2010
    Hello everyone,

    This is my first time on the forum, so please excuse my mistake if this has already been posted. Currently I am reading through the paper ``Higher Algebraic Structures and Quantization'' by D. Freed and I have a question. I section 1 (Higher Algebra I), Prof. Freed introduces the concept of a G-torsor (here G is abelian) and defines the category of G-torsors. Then he defines a multiplication and inverse structure on this category - thus giving it an ``abelian-like'' structure. He then proceeds to define a G-gerbe (or G2-torsor) as a category together with a simply transitive action of the G-torsor category - hence, mimicking what he has already done for G-torsors. However, his discussion is a bit vague for a beginner like myself. Leading to my question: Does anyone know of a reference which goes into detail about how one can construct a G2-torsor as Freed does? Thanks again.
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 24th 2010

    I am bit short with time, so for the moment I'll just say: there is the entry principal 2-bundle and the links it contains, that is about the notion of torsors over a 2-group. Looking at the entry, I see that this is very stubby, though.

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 24th 2010

    I have found Larry Breen's various notes on torsors etc. to be very helpful. There has also recently been some papers by Aldrovandi and Noohi (one already published in Advances) that gives a nice treatment. Finally the Menagerie notes by myself do have the background on this but not, I think, in the version that you can get from my n-Lab pages. Have a look at those and see if they help.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 24th 2010

    and someone please make sure that this is linked to from some nLab page...

    • CommentRowNumber5.
    • CommentAuthorrdkw10
    • CommentTimeFeb 24th 2010
    Great! Thanks a lot guys. I will start with your references immediately. Thanks again.

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