 Hopf map

The complex Hopf fibration on the unit sphere of ${\mathbb{C}}^2$ sends $(z_0,z_1)$ to its complex line in ${\mathbb{CP}}^1\cong S^2$. Its fibres are circles. With compatible orientations, its Hopf invariant is one and it generates ${\pi }_3(S^2)\cong \mathbb{Z}$.