The Klein bottle has $H_0=\ZZ$, $H_1=\ZZ\oplus\ZZ/2$, and no higher integral homology.Suggest a slogan
The integral homology groups of the Klein bottle \(K\) are \[ H_k(K;\ZZ) \cong \begin{cases} \ZZ & k = 0,\\ \ZZ\oplus\ZZ/2 & k = 1,\\ 0 & \text{otherwise} \end{cases} \] [@Hat02].
What is the homology of the Klein bottle, degree by degree?