Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: KR cohomology theory

Bottom of Page

1 to 13 of 13

  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

  1.