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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 11th 2013
    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 21st 2013
    • (edited Jun 23rd 2013)
    In the notation of the cited article, is S[BU(1)] equivalent to the connective K-theory spectrum ku?
    What about S[BU] before localization? Is it equivalent to MU or some well-known spectrum?

    Also, is there an analog for real K-theory?
    Something along the lines of ko=S[W] for some W (a naive guess would be W=BZ/2)
    and KO=ko[β^{−1}], where β is the Bott element for real K-theory (in particular, it has degree 8).
    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 22nd 2013
    Another question along the same lines: can we get other Thom spectra MG by localizing S[BG]?
    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 23rd 2013
    Also, it seems like the notation for the periodic complex cobordism spectrum is MP, whereas MU is used for the connective complex cobordism spectrum. I tried to adjust the article accordingly, but failed miserably (the Instiki engine claims “You must have Javascript on, and cookies enabled, to submit this form.”, even though I have both of them enabled).
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 23rd 2013

    The only other variant that I have seen is for periodic algebraic cobordism and algebraic K-theory, in Gepner-Snaith 08.

    Concerning notation for periodic MUMU: how about PMUPMU? I have changed it to that in the entry.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 27th 2013

    In

    • Craig Westerland, A higher chromatic analogue of the image of J (arXiv:1210.2472)

    is a tower of Snaith theorems for Morava EE-theories. Have added a pointer to this to the entry.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 4th 2013

    I have added at bit more of a remark along these lines:

    Snaith-like theorem for Morava E-theories

    also added a brief pointer along these lines to Morava E-theory itself.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 2nd 2017
    • (edited Jun 2nd 2017)

    I have expanded the section Snaith theorem – For complex topological K-theory by adding a fair amount of the basic details that go into the construction of the ring spectrum homomorphism

    Σ (BU(1) +)[β 1]KU \Sigma^\infty(B U(1)_+)[\beta^{-1}] \longrightarrow KU

    itself.

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