$\RP^4$ has $\ZZ$ in degree $0$, $\ZZ/2$ in degrees $1$ and $3$, and zero otherwise.Suggest a slogan
The integral homology groups of \(\RP^4\) are \[ H_k(\RP^4;\ZZ) \cong \begin{cases} \ZZ & k = 0,\\ \ZZ/2 & k = 1, 3,\\ 0 & \text{otherwise} \end{cases} \] [@Hat02].
What is $H_* \mathbb{RP}^4$?