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

Discussion Tag Cloud

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: equivariant stable homotopy theory

Bottom of Page

1 to 14 of 14

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 24th 2015
    • (edited Nov 25th 2015)
    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 25th 2015

    I can’t see that the Tambara functor literature has linked up with the equivariant stable homotopy theory literature very much. Isn’t this surprising, given the former is concerned with equivariant ring spectra? As Neil Strickland puts it

    Tambara functors are to rings what Mackey functors are to abelian groups.

    Rather than correspondences, they seem to deal with polynomials.

    Mike Hill discusses them in his notes for Derived Equivariant Algebraic Geometry, so I’ve added that as a reference at Tambara functor.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 25th 2015

    At equivariant homotopy group, in the section ’Definition: Via G-equivariant maps’ it talks of a subgroup HH of GG but then doesn’t use it in the definition. Should mention of HH be removed?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2015

    Thanks for catching this. So I had started out saying this in one of the two possible ways and thne switched to the other half-way. Have made it consistent now.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 12th 2016
    • (edited Jan 12th 2016)

    I have again been touching a bunch of entries related to equivariant stable homotopy theory, such as equivariant homotopy group and Mackey functor and others. Mainly I have been adding statement of and pointers to various bits of May 96. In particular at Mackey functor – cohomology I have finally started to spell out the definition of the “ordinary” cohomology of a topological G-space with coefficients in a Mackey functor.

    This was to set myself straight, for I wanted to properly convince myself of what I had previously thought was true only to then begin to worry about, namely that, for instance for G⊂Aut ℝ(ℍ)G \subset Aut_{\mathbb{R}}(\mathbb{H}) we have equivalences such as

    H (4−ℍ)+1(S 1,π 4(Σ G ∞S ℍ))≃Hom Mackey(π 5 st(S 1∧S ℍ),π 4(Σ G ∞S ℍ))≃Hom Mackey(π 4(Σ ∞S ℍ),π 4(Σ ∞S ℍ)) H^{(4 - \mathbb{H}) + 1}(S^1, \pi_4(\Sigma^\infty_G S^{\mathbb{H}})) \simeq Hom_{Mackey}( \pi^{st}_5(S^1 \wedge S^{\mathbb{H}}), \pi_4(\Sigma^\infty_G S^{\mathbb{H}}) ) \simeq Hom_{Mackey}( \pi_4(\Sigma^\infty S^{\mathbb{H}}), \pi_4(\Sigma^\infty S^{\mathbb{H}}))

    I want to eventually further clean this all up, but for tonight I do need to call it quits.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2016

    made a start at equivariant stable homotopy category and tried to improve a bit more at equivariant homotopy group and tom Dieck splitting.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 15th 2016

    Looking around related entries I guess coordinate-free spectrum should link up with G-spectrum and G-universe, no? Isn’t the ’universe’ of the former a GG-universe for the trivial group?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2016

    That’s right, coordinate-free spectra are equivalently GG-spectra indexed on a GG-universe for GG the trivial group. Yes, these entries should be interlinked better. I don’t have time to do so right now, but if you have time, please feel invited to edit!

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2019

    just noticed that the pdf link in this reference is broken now:

    • Graeme Segal, Equivariant stable homotopy theory, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, pp. 59–63. Gauthier-Villars, Paris, 1971. (pdf)

    Might anyone know a working pointer, or have the file available, that we can upload it?

    diff, v44, current

    • CommentRowNumber10.
    • CommentAuthorRodMcGuire
    • CommentTimeMay 19th 2019
    • (edited May 19th 2019)

    Might anyone know a working pointer, or have the file available, that we can upload it?

    Its in the wayback machine

    https://web.archive.org/web/20160924211120/http://www.mathunion.org/ICM/ICM1970.2/Main/icm1970.2.0059.0064.ocr.pdf

    though you probably shouldn’t link there but instead rehost it.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2019

    thanks! now uploaded and linked to here

    diff, v45, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeMar 17th 2021

    added pointer to:

    diff, v51, current

    • CommentRowNumber13.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 2nd 2023

    Added a reference

    • Tim Campion, Free duals and a new universal property for stable equivariant homotopy theory (arXiv:2302.04207)

    diff, v54, current

  14. Added reference to the second Spectral Mackey Functors paper

    Natalie Stewart

    diff, v56, current

1 to 14 of 14

  1.