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 comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite 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 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).
    • 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, https://arxiv.org/abs/2006.12374

    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