Editing Complex projective plane (section)

==Topology==
The [[Betti number]]s of the complex projective plane are

:1, 0, 1, 0, 1, 0, 0, .....

The middle dimension 2 is accounted for by the homology class of the complex projective line, or [[Riemann sphere]], lying in the plane.  The nontrivial homotopy groups of the complex projective plane are <math>\pi_2=\pi_5=\mathbb{Z}</math>.  The fundamental group is trivial and all other higher homotopy groups are those of the 5-sphere, i.e. torsion.