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nLab > Latest Changes: string 2-group

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  1.  
    • CommentRowNumber1.
    • CommentAuthorLuigi
    • CommentTimeAug 28th 2020

    Added a (sketchy) pointer to

    • Severin Bunk, Principal ∞-Bundles and Smooth String Group Models, arXiv:2008.12263

    diff, v40, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2020

    Thanks for the pointer.

    It seems to have gone largely unrecognized that the cohesive ∞-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 A of the extension could be anything, but it’s limited to being homotopy equivalent to BU(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 A not necessarily chosen to be BU(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 G such that G-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 Spin 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:

    • Andre Henriques, Integrating L∞-algebras, Compositio Mathematica, Volume 144, Issue 4 July 2008 , pp. 1017-1045 (arXiv:math/0603563, doi:10.1112/S0010437X07003405)

    diff, v43, current

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 4th 2022

    To add

    • CommentRowNumber10.
    • CommentAuthorperezl.alonso
    • CommentTimeAug 26th 2024

    Douglas-Henriques link broken, uploaded pdf file instead.

    diff, v50, current

    • CommentRowNumber11.
    • CommentAuthorperezl.alonso
    • CommentTime1 day ago
    • (edited 1 day ago)

    I came across the reference in #9, the paper is still not published and it appears the author left academia. Does anybody understand the analysis at the top of p.17? In the simplest case, that of T=U(1), the objects π0Z(U(1)J)=(ℝ⊕ℤ)/(ℤ) with the ℤ including into ℝ⊕ℤ as z↦(z,z) for simplicity, why would this become ℝ and not ℝ/ℤ? The result seems to go back to Proposition 6.1 in (FHLT ’09).

    • CommentRowNumber12.
    • CommentAuthorDavidRoberts
    • CommentTime1 day ago

    Note that R oplus Z = R times Z = coprod_Z R as sets, so you get that 0 in the n^th copy of R is identified with 1 in the (n+1)^th copy of R, not with 1 in the same copy.

    • CommentRowNumber13.
    • CommentAuthorperezl.alonso
    • CommentTime22 hours ago

    Ah, it’s like the telescope, thank you.

1 to 13 of 13

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