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I have started rational equivariant stable homotopy theory, but so far there is nothing but references.
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.
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.
I added that first item mentioned in #2:
It only came out last week.
Thanks. And I just fixed a typo in #3: of course the Dihedral group sits in $O(2) \hookrightarrow SO(3)$, not in $SO(2)$.
added pointer to:
added pointer to:
Anna Marie Bohmann, Christy Hazel, Jocelyne Ishak, Magdalena Kędziorek, Clover May, Naive-commutative structure on rational equivariant K-theory for abelian groups (arXiv:2002.01556)
Anna Marie Bohmann, Christy Hazel, Jocelyne Ishak, Magdalena Kędziorek, Clover May, Genuine-commutative ring structure on rational equivariant K-theory for finite abelian groups (arXiv:2104.01079)
added pointer to:
(previously we just had a pointer to the thesis of a similar title)
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