Smooth structures on $\mathbb{C}{P}^m$ for $5\le m\le 8$

Ramesh Kasilingam

We classify up to diffeomorphism all smooth manifolds homeomorphic to the complex projective m-space $\mathbb{C}{P}^m$ for $m=5,6,7$ and $8$. As an application, for $m=7$ and…