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    • CommentRowNumber1.
    • CommentAuthorLuigi
    • CommentTimeAug 28th 2020

    Added a (sketchy) pointer to

    diff, v40, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2020

    Thanks for the pointer.

    It seems to have gone largely unrecognized that the cohesive \infty-topos-theoretic discussion of the String 2-group is in section 5.1.4 of dcct (p. 583).

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 28th 2020

    Reading that sounds as though the AA of the extension could be anything, but it’s limited to being homotopy equivalent to BU(1)B U(1), right?

    Triple adjunction rather than adjoint quadruple, hmm.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2020
    • (edited Aug 28th 2020)

    Yes, on p. 29-30:

    [ our definition ] is a generalisation as well as a weakening of the following approach to smooth string group extensions (see, for instance, [FRS16]):

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 28th 2020

    Ok, so have added

    with AA not necessarily chosen to be BU(1)\mathbf{B}U(1) but only of the same homotopy type, …

    diff, v41, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2020

    By the way, I think this perspective that the String 2-group, even in the smooth case, “was defined” to be a 3-connected cover is misled:

    By it’s very name, the String 2-group is meant to be that GG such that GG-structure encodes cancellation of the Green-Schwarz anomaly.

    That for the global GS anomaly (i.e. disregarding differential structure) this is given by a 3-connected cover of the homotopy type pf SpinSpin is a noteworthy phenomenon, but not the definition.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2020

    added publication data for:

    diff, v43, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2020

    added publication data for:

    diff, v43, current

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