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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 20th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have started _[[rational equivariant stable homotopy theory]]_, but so far there is nothing but references.

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

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 20th 2015
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   Author: David_Corfield
   Format: MarkdownItexI see they're pushing on to $SO(3)$, as mentioned in [Rational SO(2)-Equivariant Spectra](http://arxiv.org/abs/1511.03291) >M. Kedziorek. An algebraic model for rational SO(3) - spectra. In preparation.

   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.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 21st 2015
   • (edited Nov 22nd 2015)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for the pointer! Apparently this is a thesis which is out be now, see [here](http://etheses.whiterose.ac.uk/7699/). 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.

   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.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 21st 2015
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI added that first item mentioned in #2: * [[David Barnes]], [[John Greenlees]], [[Magdalena Kedziorek]], [[Brooke Shipley]], _Rational SO(2)-Equivariant Spectra_ ([arXiv:1511.03291](http://arxiv.org/abs/1511.03291)) It only came out last week.

   I added that first item mentioned in #2:

   • David Barnes, John Greenlees, Magdalena Kedziorek, Brooke Shipley, Rational SO(2)-Equivariant Spectra (arXiv:1511.03291)

   It only came out last week.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 22nd 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. And I just fixed a typo in #3: of course the Dihedral group sits in $O(2) \hookrightarrow SO(3)$, not in $SO(2)$.

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

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeSep 10th 2020
   • (edited Sep 10th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[David Barnes]], [[Magdalena Kedziorek]], _An introduction to algebraic models for rational G-spectra_ ([arXiv:2004.01566](https://arxiv.org/abs/2004.01566)) <a href="https://ncatlab.org/nlab/revision/diff/rational+equivariant+stable+homotopy+theory/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+equivariant+stable+homotopy+theory/18">v18</a>, <a href="https://ncatlab.org/nlab/show/rational+equivariant+stable+homotopy+theory">current</a>

   added pointer to:

   • David Barnes, Magdalena Kedziorek, An introduction to algebraic models for rational G-spectra (arXiv:2004.01566)

   diff, v18, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 3rd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded 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](https://arxiv.org/abs/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](https://arxiv.org/abs/2104.01079)) <a href="https://ncatlab.org/nlab/revision/diff/rational+equivariant+stable+homotopy+theory/22">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+equivariant+stable+homotopy+theory/22">v22</a>, <a href="https://ncatlab.org/nlab/show/rational+equivariant+stable+homotopy+theory">current</a>

   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)

   diff, v22, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeDec 22nd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Magdalena Kedziorek]], _An algebraic model for rational $SO(3)$–spectra_, Algebraic & Geometric Topology 17 (2017) 3095–3136 ([arXiv:1611.08415](https://arxiv.org/abs/1611.08415), [doi:10.2140/agt.2017.17.3095](https://doi.org/10.2140/agt.2017.17.3095)) (previously we just had a pointer to the thesis of a similar title) <a href="https://ncatlab.org/nlab/revision/diff/rational+equivariant+stable+homotopy+theory/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/rational+equivariant+stable+homotopy+theory/24">v24</a>, <a href="https://ncatlab.org/nlab/show/rational+equivariant+stable+homotopy+theory">current</a>

   added pointer to:

   • Magdalena Kedziorek, An algebraic model for rational $SO(3)$–spectra, Algebraic & Geometric Topology 17 (2017) 3095–3136 (arXiv:1611.08415, doi:10.2140/agt.2017.17.3095)

   (previously we just had a pointer to the thesis of a similar title)

   diff, v24, current