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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 16th 2020

    starting some minimum

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 24th 2020
    • (edited Jun 24th 2020)

    added these pointers:

    A more geometric model of orbifold K-theory in terms of bundles of Fredholm operators over Lie groupoids/differentiable stacks:

    Review in:

    The claim that these two definitions are equivalent, in that this groupoid K-theory reduces to equivariant K-theory on global quotient orbifolds, is Freed-Hopkins-Teleman 07, Prop. 3.5.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 25th 2020

    I don’t know where you want to put this new article, but it looks relevant:

    Branko Juran, Orbifolds, Orbispaces and Global Homotopy Theory,

    It’s from a student of Schwede. I haven’t seen you mention it, so apologies if you have seen this already.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 25th 2020

    Thanks, I had missed that.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 25th 2020

    Okay, I have added the pointer to the entry, as follows:

    The suggestion (Schwede 17, Intro, Schwede 18, p. ix-x) that orbifolds should be regarded as orbispaces in global equivariant homotopy theory and then their orbifold cohomology be given by equivariant cohomology with coefficients in global equivariant spectra is worked out for (Bredon cohomology and) orbifold K-theory in:

    • Branko Juran, Orbifolds, Orbispaces and Global Homotopy Theory (arXiv:2006.12374)

    Example 5.31 there shows that on global quotient orbifolds this is again equivalent to the previous definitions.

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2020

    I have added pointer to the “full orbifold K-theory” of

    They prove it agrees with Adem-Ruan (and hence with all other definitions) on global quotients. I guess this means it agrees with Freed-Hopkins-Teleman and Juran in general? Does anyone discuss this?

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 30th 2021
    • (edited Jul 30th 2021)

    Added pointer to

    diff, v11, current