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nLab > Latest Changes: KR cohomology theory

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2019
    • (edited Sep 15th 2019)

    for the equivariant+twisted version I added further pointer to

    diff, v33, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 15th 2019
    • (edited Sep 15th 2019)

    I have reservations about that paper of Moutuou.

    In this paper it is pointed out in footnote 1 on page 5 that the concrete examples therein

    …seem to be at odds with the results of [7] if their correspondence between Real continuous trace C *C^*-algebras and Real bundle gerbes is a straightforward generalisation of the complex case.

    where the paper [7] (here) says “Moutuou’s classification of possible twists of KR coincides with ours”, and cite his paper in #1. It is my understanding that the quote above is very carefully phrased.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2019
    • (edited Sep 15th 2019)

    Thanks for highlighting. Yes, it has been the comment in [7] that led me to Moutuou.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 15th 2019
    • (edited Sep 15th 2019)

    I’m not sure, but Richard Szabo or Pedram Hekmati might know. (Edit this was in response to a now-deleted reference request)

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2019
    • (edited Sep 15th 2019)

    Thanks, yeah, after writing it I saw how they did it.

    I may sure contact the authors, but maybe you know sbout the following already: In the intro they recall the open problems with O-plane charge in KR. Do they then claim to solve these or just to clarify the issues?

    I still need to read in more detail…

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 15th 2019

    I think the idea was really to make some concrete calculations to clarify the situation about the possible twists of KR-theory, following up on this paper, given the confusion around the existing literature. This earlier paper is more theory-oriented.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2019

    Thanks, I have read it now. I see.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2019

    Hm, few of these and related articles seem to have been published. (?)

    • CommentRowNumber9.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 15th 2019

    As far as the Hekmati et al papers go, the first is to appear in ATMP, the second still under consideration at a journal. Or are you talking about the papers in #1?

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeSep 16th 2019

    Thanks, I’ll put “to appear in ATMP” then.

    • CommentRowNumber11.
    • CommentAuthorGuest
    • CommentTimeAug 10th 2021
    "But on abstract grounds maybe KR-theory would best be just called Z2-equivariant complex K-theory."

    I think that name is incorrect. Z2-equivariant complex K-theory is already the name of something; it is the Grothendieck group of complex vector bundles over a Z2-space equipped with a complex-linear lift of the involution. Real K-theory has instead a complex antilinear lift. Atiyah points this out explicitly in the original paper.
    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeAug 11th 2021

    Thanks for the alert. True, I have removed that line.

    diff, v38, current

    • CommentRowNumber13.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 11th 2021

    Publication details for

    diff, v39, current

1 to 13 of 13

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