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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 $MU$: how about $PMU$? 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 $E$-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

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

itself.

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