Timeline for Why are equivariant homotopy groups not RO(G)-graded?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| May 17, 2011 at 23:21 | comment | added | Tom Goodwillie | I'm glad you asked the question. Answering it clarified things for me a little. | |
| May 17, 2011 at 22:24 | comment | added | Dylan Wilson | Right, this is sort of what I expected the answer to be related to; I guess I just saw "Hey that 'n' got generalized to a 'V' since integers should mean dimensions of vector spaces... so why didn't that other 'n' get generalized to a 'V'?" and I suppose you're answer is "Because that 'n' means a different thing than the other 'n' because it comes from using spheres in a different way." | |
| May 17, 2011 at 16:58 | comment | added | Tom Goodwillie | The question was about the stable theory ($G$-spectra). The answer was about $G$-spaces. It applies to $G$-spectra, too, once the right definitions have made. Of course, representation spheres occur in the stable theory in another way, too. Nonequivariantly spheres play two different central roles in homotopy, don't they? On the one hand, they lead to cell complexes, and on the other hand smashing with spheres leads to spectra. Equivariantly the $S^n\wedge G/H_+)$ play the first role while the representation spheres play the second role. | |
| May 17, 2011 at 16:10 | comment | added | Dylan Wilson | This explanation definitely convinced me. I want G-manifolds! (And I don't want to pay more for them.) | |
| May 17, 2011 at 16:09 | vote | accept | Dylan Wilson | ||
| May 17, 2011 at 13:23 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
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| May 17, 2011 at 11:20 | history | answered | Tom Goodwillie | CC BY-SA 3.0 |