Timeline for A $d_1$-differential in the homotopy fixed points spectral sequence
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2020 at 11:38 | comment | added | Igor Sikora | Of course, I see now. Thanks! | |
| Nov 18, 2020 at 0:05 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Nov 17, 2020 at 22:34 | comment | added | Bertram Arnold | I made a mistake in the last part of the comment: the Serre SS I described is the spectral sequence converging to homotopy groups of the homotopy orbits $X_{hG}$. For fixed points, you essentially do the same construction of filtering $EG$ with an equivariant CW structure, coming eg from the realization of the nerve of $G//G$; the $E_1$-page is the standard cobar complex computing group cohomology with values in $\pi_*(X)$. Again, this only depends on the naive equivariant structure, i.e. the functor $BG\to Sp$, and the HFPSS is the Serre-Atiyah-Hizebruch SS computing twisted $X$-cohomology. | |
| Nov 17, 2020 at 21:21 | comment | added | Bertram Arnold | You have constructed an explicit $C_2$-CW-structure on $\mathbb S(\infty)$, which is a model for $EC_2$ (contractible with free action). Namely, you have one cell $C_2\times D^n$ in each dimension, which are the north and south hemisphere attached to the equator. The differential is given by the degrees of the attaching maps; to get the signs, note that this CW structure comes from the realization of the nerve of the category $C_2//C_2$ (two isomorphic objects). In fact, the HFPSS does not depend on the genuine $C_2$-structure, and is the Serre SS of the fibration $EC_2\times_{C_2}X\to BC_2$. | |
| Nov 17, 2020 at 20:02 | history | asked | Igor Sikora | CC BY-SA 4.0 |