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May 18, 2011 at 13:09 comment added Tom Goodwillie The point should also be made that the obvious analogue of Elmendorf's theorem for spectra does not hold for the "fancy" theory.
May 18, 2011 at 13:09 comment added Tom Goodwillie I don't think that there is any reason why representation spheres have to appear in the foundations of a homotopy theory of $G$-spaces. They occur naturally when you look at $G$-manifolds. For $G$-spectra they are usually built into the definition, and I imagine there is more than good viewpoint as to why they should.
May 17, 2011 at 21:50 history answered Mike Shulman CC BY-SA 3.0