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nLab > Latest Changes: twisted K-theory

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2011

    am slowly starting to add some genuine content to twisted K-theory

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 18th 2011

    added the statement (just the statement) of the CBMMS-theorem on how twisted K-theory is K-theory of twisted bundles.

    Touched lifting gerbe and gerbe module.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 29th 2012

    have added to twisted K-theory some of the classical references that were missing there

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 24th 2014

    of all definitions, the one by Fredholm bundles had been missing in the entry twisted K-theory. Have added something now here.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 2nd 2020

    added this pointer:

    The general definition of twisted K-theory in terms of sections is fully explicit in:

    diff, v45, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMar 15th 2021
    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 31st 2021

    added (here) some references on higher twists

    diff, v60, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2022

    added pointer to the original reference (I think) on the twist of KU in degree 1:

    • Ellen Maycock Parker, The Brauer Group of Graded Continuous Trace C *C^\ast-Algebras, Transactions of the American Mathematical Society 308 1 (1988) [jstor:2000953]

    (this has been references at PU(ℋ) all along, but should also be cited here)

    diff, v67, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 18th 2023

    added pointer to:

    diff, v71, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2023
    • (edited Nov 18th 2023)

    added this pointer:

    • Ulrich Pennig, Equivariant Higher Twisted K-Theory of SU(n)SU(n) via Exponential Functors, talk at CQTS (20 Sep 2023) [video:YT]

    diff, v72, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 22nd 2025
    • (edited Jun 22nd 2025)

    Added below the bibitem Atiyah & Segal 2004 the warning:

    (beware of the false claim in AS04 p 39 that U(ℋ)U(\mathcal{H}) in the compact open topology is not a topological group, corrected by Schottenloher 2013, Espinoza & Uribe 2014, going back to Schottenloher 1995)

    also at equivariant K-theory, twisted equivariant K-theory and on the author’s pages.

    This issue used to be pointed out all along at U(H), but due to the prominence of the article it’s better to have this warning with each occurrence.

    diff, v79, current

    • CommentRowNumber12.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 24th 2025

    The false claim that U(H) is not a group in the strong operator topology goes back to Simms 1968 book “Lie Groups and Quantum Mechanics”. Let’s give credit where it’s due!

1 to 12 of 12

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