In *Homology of $C_{n+1}$-spaces, $n\geq 0$,* F.R. Cohen, *Lecture Notes in Mathematics, Vol. 533,* Chapter 5, 6, 7, 8, 9, 10, 11, the cohomology algebra $H^*(B(\mathbb{R}^{n+1},p),\mathbb{Z}_p)$, for $p$ prime and $B(\mathbb{R}^{n+1},p)=F(\mathbb{R}^{n+1},p)/\Sigma_p$, is obtained. A spectral sequence for fibration $\Sigma_p\to F(\mathbb{R}^{n+1},p)\to B(\mathbb{R}^{n+1},p)$ is used with the action of $\Sigma_p$ on $H^*(F(\mathbb{R}^{n+1},p);\mathbb{Z})$.

For other manifolds $M$ such as $S^m$ and $S^m\times \mathbb{R}^k$ ($H^*F(\mathbb{R}^{n+1},p;\mathbb{Z}_p)$ is known in these cases), are there any results for the cohomology algebra $H^*(B(M,p);\mathbb{Z}_p)$ in any references? Thanks!