Timeline for Cochains on Eilenberg-MacLane Spaces
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2010 at 20:14 | comment | added | Jacob Lurie | That's the strategy I had in mind. When n=0 you can prove it using deformation theory, so let's try induction on n. Let R(n) be the cofiber and let R'(n) be the cochains on K(Z/pZ,n). Then doing a bar construction on R(n) produces R(n-1), and similarly for R'(n). So the I.H. tells you that the map R(n) -> R'(n) is an equivalence after applying the bar construction. If you knew that R(n) had no positive homotopy and that pi_0 R(n) = k (statements which are obvious for R'(n)), then the bar construction doesn't lose any information and you are done. But a priori R(n) is a big mess. | |
| Dec 3, 2010 at 19:51 | comment | added | Charles Rezk | Toen's technique seems to involve an inductive approach, using the result for $X=K(Z/pZ,n)$ to prove it for $BX=K(Z/pZ,n+1)$. Could that be used here to reduce to the case of $n=1$ or $n=0$? | |
| Dec 3, 2010 at 17:11 | comment | added | Jacob Lurie | He also doesn't prove this theorem. Unless I misunderstand, he works in the setting of cosimplicial algebras (where the analogous statement is easy) and uses it to prove variants of Mandell's results. | |
| Dec 3, 2010 at 16:02 | comment | added | Ben Wieland | Bertrand Toen doesn't seem to do much calculation in Champs affines. | |
| Dec 3, 2010 at 5:00 | history | asked | Jacob Lurie | CC BY-SA 2.5 |