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nLab > Latest Changes: Bibundle

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 25th 2010

    Started on bibundles, but there seem to be a raft of competing definitions. Perhaps they're all special cases of a most general definition.

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeJun 25th 2010

    I put in a line about the general meaning of the term, but I didn’t try to give a precise definition that everything on the page is a special case of.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2010

    Hopefully eventually somebody finds the time to describe how principal bibundles are really groupoid-principal bundles. But it’s not me right now. Thomas and Konrad want to be coming out with a paper on this in the near future.

  4. So the kind of Bibundles which show up in non-abelian bundle gerbes (i.e. bundles over a space X with two commuting actions of G making it principle) are a special case of the notion of bibundles between Lie groupoids. This is mentioned briefly in my String group paper on the arXiv:0911.2483. In particular Example 14 shows how this translation works.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2010

    Chris,

    if you put this remark into the nLab entry bibundle, it will be preserved for eternity. At least Google will have an easier time pointing people to it.

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