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