Timeline for Homology of iterated loop spaces on odd--dimensional spheres
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 7, 2022 at 11:51 | vote | accept | Victor | ||
| Dec 7, 2022 at 0:18 | comment | added | John Palmieri | @Tyrone: presumably you mean the homology of $\Omega^3 S^{2n+1}$, not the homology of $S^{2n+1}$. | |
| Dec 6, 2022 at 22:06 | comment | added | Nicholas Kuhn | As has already been said, Cohen, Lada, May - see the part by Fred Cohen - has this and more. But this particular calculation (at least for p=2) goes back much further: Bill Browder's 1958 thesis, turned into a 1960 Illinois Journal of math article, calculates precisely this, and introduces the `Browder operations' enroute. | |
| Dec 6, 2022 at 21:33 | comment | added | Tyrone | For anyone without a copy of Cohen-Lada-May, for $p$ odd and $n\geq2$ they calculate $H_*(S^{2n+1};\mathbb{F}_p)\cong\mathbb{F}_p[Q^a_{2(p-1)}u_{2n-2}\mid a\geq0]\otimes E(Q^a_{p-1}\beta Q^b_{2(p-1)}u_{2n-2}\mid a\geq0,b>0)\otimes \mathbb{F}_p[\beta Q^a_{p-1}\beta Q^b_{2(p-1)}u_{2n-2}\mid a,b>0]$ | |
| Dec 6, 2022 at 21:03 | history | answered | Neil Strickland | CC BY-SA 4.0 |