Timeline for (∞, 1)-categorical description of equivariant homotopy theory
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| May 18, 2010 at 16:31 | comment | added | Tony Elmendorf | Mark, the paper of mine you're remembering is the one joint with Peter May, "Algebras over equivariant sphere spectra", JPAA 116 (1997) 139-149. It shows that, indeed, you can consider just one underlying category of G-spectra with a number of (cofibrantly generated) model structures on it. The "change of universe" functors usually considered from the Lewis-May-Steinberger point of view are then simply the derived functors of the identity functor. The category itself is the EKMM category with G acting in the obvious way on the objects. -- Tony Elmendorf | |
| Nov 23, 2009 at 16:02 | comment | added | Tyler Lawson | I ... don't think so. If you did this to spaces, you'd be decreeing that the map S^0 -> N_+ is a weak equivalence, and this annihilates S^0. You want to invert the suspension operator instead, but if you invert maps X -> Y that become equivalences after suspension you are only picking out suspension spectra. | |
| Nov 23, 2009 at 14:19 | comment | added | Mark Hovey | I was afraid someone would ask this. So the answer is that I don't know and I might be wrong. However, S^V is a G-space, right, so can't I declare the map X --> Omega^V S^V X a weak equivalence? Here I am just using the enrichment of G-spectra over G-spaces. Of course, I would have to do this carefully to be sure I got a model structure. Again, I am not sure this is right. | |
| Nov 23, 2009 at 5:42 | comment | added | Tyler Lawson | Perhaps I'm not aware of the issues, but how could a localization provide a sequence of deloopings for representation spheres? | |
| Nov 17, 2009 at 18:13 | history | answered | Mark Hovey | CC BY-SA 2.5 |