Let $M$ be a connected compact closed 4 manifold. Then $H_4(M)=\mathbb{Z}$. If we assume it is smooth, from Morse theory we know that $M$ has a CW structure. But can we find a CW structure of $M$ with only one 4-cell?

Moreover, assume we drop the smoothable condition of $M$. I would like to know under what circumstances $M$ is homotopy equivalent to a CW complex with only one 4-cell? Thank you.