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Mar 11, 2021 at 23:30 comment added Andy Jiang Though I'm not so sure what the $E_2$ structure on the final thing is.
Mar 11, 2021 at 23:28 comment added Andy Jiang I also somehow forgot this simple fact when I wrote the question.
Mar 11, 2021 at 23:28 comment added Andy Jiang I think it's the same as $H^*(\Omega S^3,\mathbb{F}_p)$ because $\mathbb{F_p}^{\Omega^2 S^3} \cong \lim_{\Omega S^3}{\mathbb{F}_p}$ and the latter is $Hom(\Sigma^{\infty} \Omega S^3,\mathbb{F}_p)$ where I meant Hom in spectra, which is the cohomology of $\Omega S^3$ in $\mathbb{F}_p$ coefficients
Mar 11, 2021 at 22:20 comment added Jonathan Beardsley Silly question, but how does $\mathbb{F}_p^{\Omega^2S^3}$ relate to $H^\ast(\Omega^2 S^3; \mathbb{F}_p)$?
Mar 11, 2021 at 20:22 vote accept Andy Jiang
Mar 11, 2021 at 20:11 answer added John Rognes timeline score: 8
Mar 11, 2021 at 19:41 history edited YCor CC BY-SA 4.0
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Mar 11, 2021 at 18:54 history asked Andy Jiang CC BY-SA 4.0