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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 20th 2015

I have started rational equivariant stable homotopy theory, but so far there is nothing but references.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeNov 20th 2015

I see they’re pushing on to $SO(3)$, as mentioned in Rational SO(2)-Equivariant Spectra

M. Kedziorek. An algebraic model for rational SO(3) - spectra. In preparation.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 21st 2015
• (edited Nov 22nd 2015)

Thanks for the pointer! Apparently this is a thesis which is out be now, see here. Am adding it to the entry now.

What I am actually after is equivariance with respect to finite subgroups of $SO(3)$. But of course some of them factor through the inclusion $O(2) \hookrightarrow SO(3)$, the cyclic groups and the dihedral groups. Moreover, I am after seeing whether the quaternionic Hopf fibration with its canonical action by $SO(3)$ becomes a non-torsion element for any of these subgroups, in the corresponding RO(G)-degree 3. If that works for the cyclic groups of the dihedral groups, then it will be visible already in just $SO(2)$-equivariant homotopy theory.

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeNov 21st 2015

I added that first item mentioned in #2:

It only came out last week.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeNov 22nd 2015

Thanks. And I just fixed a typo in #3: of course the Dihedral group sits in $O(2) \hookrightarrow SO(3)$, not in $SO(2)$.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeSep 10th 2020
• (edited Sep 10th 2020)